abscissa

en-noun

abscissa (plural abscissas or abscissae or abscissæ)

abscissas (plural)
abscissae (plural)
abscissæ (plural)

By ellipsis from Latin [linea] abscissa, feminine of abscissus, perfect passive participle of abscindō (“cut off”). See abscind.

The point (3,2) has 3 as its abscissa and 2 as its ordinate.

(geometry) The first of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.

(geometry) The horizontal line representing an axis of a Cartesian coordinate system, on which the abscissa (sense above) is shown.


accidental

en-adj

accidental (comparative more accidental, superlative most accidental)

more accidental (comparative)
most accidental (superlative)
accidentall (alternative obsolete)

From Middle English accidental, from Anglo-Norman accidentel, Middle French accidentel, accidental, and their source, Late Latin accidēntālis; corresponding to accident + -al.

(geometry) Being a double point with two distinct tangent planes in 4-dimensional projective space.


lens

en-noun

lens (plural lenses or (obsolete) lens or (rare) lentes)

lenses (plural)
lens (obsolete plural)
lentes (plural rare)
lense (alternative)

→ Bengali: লেন্স (lenś)

→ Turkish: lens

Borrowed from Latin lēns (“lentil”), with Medieval Latin later taking on the sense of “lens”, a semantic loan from Arabic عَدْسَة (ʕadsa, “lentil; optic lens”).

semantic loan

(geometry) A convex shape bounded by two circular arcs, joined at their endpoints, the corresponding concave shape being a lune.

lens

geometry: convex shape bounded by two circular arcs


star

Sranan Tongo: stari
Aukan: sitali

→ Finnish: stara

→ French: star

→ German: Star

→ Italian: star

→ Swahili: staa

From Middle English sterre, from Old English steorra (“star”), from Proto-West Germanic *sterrō, variant of *sternō, from Proto-Germanic *sternô, *sternǭ (“star”), from Proto-Indo-European *h₂stḗr (“star”). Doublet of aster, stella, étoile, and estoile.
Cognates
Cognate with Scots starn, ster, North Frisian steer, West Frisian stjer, Saterland Frisian Stiern, Dutch ster, Luxembourgish Stär, German Stern, Yiddish שטערן (shtern), Vilamovian śtaom, Swedish stjärna, Norwegian stjerne, Icelandic stjarna, Gothic 𐍃𐍄𐌰𐌹𐍂𐌽𐍉 (stairnō), Spanish estrella, Portuguese estrela, French étoile, Italian stella, Romanian stea, Occitan estela, Venetan stéła, Sicilian stidda, Sardinian isteddu, Mirandese streilha, Walloon sitoele, Romansch staila, Megleno-Romanian steau̯ă, Istriot stila, Istro-Romanian ste, Latin stēlla, Greek αστέρι (astéri), Ancient Greek ἀστήρ (astḗr), Old Armenian աստղ (astł), Persian ستاره (setâre), Tajik ситора (sitora), Pashto ستوری (storay), Mazanderani اساره (ëssâre), Northern Kurdish stêr, Central Kurdish ئەستێرە (estêre), Zazaki astare, Ossetian стъалы (st’aly), Hindi तारा (tārā), Urdu تارا (tārā), Punjabi ਤਾਰਾ (tārā), Gujarati તારો (tāro), Sanskrit तारा (tārā).

аеҵǝа

a celestial body appearing as a point of light on the clear night sky, whose position is relatively fixed with respect to each other

(geometry) A concave polygon with regular, pointy protrusions and indentations, usually with four, five, or six points.


pencil

pencils (plural)
pensill (alternative obsolete)

Tok Pisin: pensil

→ Bole: pensur

→ Central Dusun: pinsil

→ Central Melanau: pisil

→ Dhivehi: ފަންސުރު (fan̊suru)

desc

→ Gulf Arabic: بِنْسِل (pinsil, binsil) (obsolete)

→ Hausa: fensir

→ Hindi: पेंसिल (pensil), पेन्सिल (pensil)

→ Iban: pinsil

→ Indonesian: pènsil

→ Maguindanao: pinsil

or via Tok Pisin <i class="Latn mention" lang="tpi">pensil</i>

→ Maia: pensil (or via Tok Pisin pensil)

→ Malay: pensel

→ Malayalam: പെൻസിൽ (peṉsil)

→ Marshallese: pinjeļ

→ Pennsylvania German: Bensil

→ Scottish Gaelic: peansail

→ Swahili: penseli

→ Swazi: ípénseli

→ Tagalog: pensil

→ Tausug: pinsil

→ Telugu: పెన్సిలు (pensilu)

→ Welsh: pensil, pensel

→ Xhosa: ípénsile

→ Yoruba: pẹ́ńsù

From Anglo-Norman and Old French pincil (see the variant pincel, which gave rise to Modern French pinceau (“paintbrush”)), from Latin pēnicillum, diminutive of pēniculus (“brush”), itself a diminutive of pēnis (“tail; penis”). Not related to pen.

When, by the pencil becoming oblique to the surface, the vergency produced on the pencil becomes changed, the primary and secondary focal points, V and H, separate […]

1863, The Civil Engineer and Architect's Journal:

A drillable robot is capable of placing its end link in any orientation in the pencil of planes containing its first link.

1987, R. E. Trahan, Applied Identification, Modelling and Simulation, page 107:

Let l and m be two hyperparallel lines. All the transversals to l and m that form congruent corresponding angles with l and m lie in a pencil.

2012, G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, page 357:

(geometry) A family of geometric objects with a common property, such as the set of lines that pass through a given point in a projective plane.


apple

qualifier

< <i class="Latn mention" lang="en">apples</i>

→ Abenaki: aples (< apples)

→ Arikara: ápos (< apples)

→ Assamese: আপেল (apel)

→ Bengali: আপেল (apel)

→ Dhivehi: އާފަލު (āfalu)

→ Dzongkha: ཨེ་པཱལ (e pāl)

→ East Futuna: apo

→ Fijian: yapolo

→ Fiji Hindi: aapul

→ Finnish: äpyli

→ Malay: epal (Malaysia)

→ Malayalam: ആപ്പിൾ (āppiḷ)

→ Maori: āporo

→ Marshallese: abōļ

→ Sinhalese: ඇපල් (æpal)

→ Sotho: apole

Sylheti: ꠀꠄꠚꠟ (aefól)

→ Tamil: ஆப்பிள் (āppiḷ)

→ Telugu: ఆపిల్ (āpil)

desc

→ Thai: แอปเปิล (ɛ́p-bpə̂n)

→ Thai: แอปเปิล (ɛ́p-bpə̂n)

→ Tokelauan: apu

→ Tok Pisin: apel

→ Yurok: 'erplers (< apples)

Book of Genesis
Frans Floris
Malmö Art Museum
The Fall of Man

Etymology tree
Proto-Indo-European *h₂ébōl
Proto-Germanic *aplaz
Proto-West Germanic *applu
Old English æppel
Middle English appel
English apple
The noun is derived from Middle English appel (“Malus domestica fruit or tree, apple; any type of fruit, nut, or tuber; tree bearing fruit; (figurative) ball, sphere; (Christianity) forbidden fruit in Eden”), from Old English æppel (“apple; any type of fruit; (figurative) ball, sphere; eyeball”), from Proto-West Germanic *applu (“apple; any type of fruit”), from Proto-Germanic *aplaz (“apple; any type of fruit”), from Proto-Indo-European *h₂ébōl, *h₂ébl̥ (“apple”).
As regards sense 1.4 (“forbidden fruit”), the type of fruit eaten by Adam and Eve is not identified in the Book of Genesis in the Bible. It may have come to be identified with the apple because of the similarity between Latin mālum (“apple”) and malum (“evil; misery, torment; wrongdoing”).
The verb is derived from the noun.
Cognates
Cognate with Danish æble, Dutch appel, German Apfel, Irish úll, Lithuanian óbuolỹs, Russian я́блоко (jábloko), Scots aipple, Swedish äpple, Welsh afal, West Frisian apel, possibly Ancient Greek ἄμπελος (ámpelos, “vine”).

ref

From the collection of the Malmö Art Museum in Malmö, Scania, Sweden.

omena

something which resembles the fruit of Malus domestica

the apple doesn't fall far from the tree

the apples on the other side of the wall are the sweetest

Malus domestica
Malus domestica#Translingual

surface of revolution
surface of revolution

A common, firm, round fruit produced by a tree of the genus Malus.

Something which resembles the fruit of Malus domestica (sense 1.1) in shape (such as a ball, breast, or globe) or colour.

(geometry) The surface of revolution of a circular arc of an angle greater than 180° rotated about the straight line passing through the arc's two endpoints.


absolute

absolutes (plural)
abs. (alternative)
absolut (alternative)

First attested around 1380. From Middle English absolut, from Middle French absolut, from Latin absolūtus (“unconditional; unfettered; completed”), perfect passive participle of absolvō (“loosen, set free, complete”), from ab (“away”) + solvo (“to loose”). Influenced in part by Old French absolu. Compare absolve.

der

(geometry) In a plane, the two imaginary circular points at infinity; in space of three dimensions, the imaginary circle at infinity.


translationary

LL-Q1860 (eng)-Flame, not lame-translationary.wav

(geometry) Pertaining to the shifting of coordinate axes.


dual

duals (plural)
du. (alternative abbreviation)

PIE word
 *dwóh₁
Borrowed from Latin dualis (“two”), from duo (“two”) + adjective suffix -alis.

The octahedron is the dual of the cube.

(geometry) Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.


cube

From Old French cube, from Latin cubus, from Ancient Greek κύβος (kúbos).

(geometry) A regular polyhedron having six identical square faces.

kubus

geometry: polyhedron having of six identical square faces


hexahedron

en-noun

hexahedron (plural hexahedrons or hexahedra)


perpendicular

en-adj

perpendicular (comparative more perpendicular, superlative most perpendicular)

more perpendicular (comparative)
most perpendicular (superlative)

Derived from Middle French perpendiculaire, from Old French perpendiculer, from Latin perpendiculum (“plumb line”).

der+

In most houses, the walls are perpendicular to the floor.

A doorknob of whatever roundish shape is effectively a continuum of levers, with the axis of the latching mechanism—known as the spindle—being the fulcrum about which the turning takes place. Applying a force tangential to the knob is essentially equivalent to applying one perpendicular to a radial line defining the lever.

2012 March 18, Henry Petroski, “Opening Doors”, in American Scientist, volume 100, number 2, pages 112–3:

(geometry) At or forming a right angle (to something).


perpendicular

(geometry) A line or plane that is perpendicular to another.


triangle

/ˈtɹaɪəŋɡəl/

/ˈtɹaɪˌæŋɡəl/

/ˈtɹaɪˌæŋɡəl/

PIE word
 *tréyes
From Middle English triangle, from Old French triangle, from Latin triangulum, noun use of adjective triangulus (“three-cornered, having three angles”), from trēs (“three”) + angulus (“corner, angle”), equivalent to tri- + angle.

The wedge-shaped character was the triangle, the archaic Paleolithic sign of the vulva; the pubic triangle was at the end of the phallic stylus.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 22:

(geometry) A polygon with three sides and three angles.


polygon

From Ancient Greek πολύγωνον (polúgōnon), from πολύς (polús, “many”) + γωνία (gōnía, “angle”).

(geometry) A plane figure bounded by edges that are all straight lines.

(geometry) The boundary of such a figure.

(geometry, more generally) A figure comprising vertices and (not necessarily straight) edges, alternatingly.

(geometry) Such a figure and its interior, taken as a whole.


square

→ Welsh: sgwâr

From Middle English square, sqware, squyre; from Old French esquarre, esquerre, (modern French équerre), from Vulgar Latin *exquadra, from Latin ex- + quadro, from quadrus (compare English quad and quadra). Doublet of squad and squadra.
Displaced Old English fēowerecge (fēower nominative + ecg accusative, as in "four-edged").

I took refuge in the square form and exhibited a picture which consisted of nothing more than a black square on a white field.

1927, Kazimir Malevich, The Non-Objective World:

(geometry) A polygon with four straight sides of equal length and four right angles; an equilateral rectangle; a regular quadrilateral.


square

en-verb

square (third-person singular simple present squares, present participle squaring, simple past and past participle squared)

squares (present singular third-person)
squaring (participle present)
squared (participle past)
squared (past)

подравнявам

to adjust so as to align with or place at a right angle

jalustaa poikittain

nautical: to place at right angles with the keel

square the circle

(transitive, geometry) To draw, with a pair of compasses and a straightedge only, a square with the same area as.

neliöidä

geometry: to draw a square with same area as something else

(transitive, geometry) To tile (completely fill) with squares.


trapezoid

/ˈtɹæpəzɔɪd/

/ˈtɹæpəzɔɪd/

From Ancient Greek τραπέζιον (trapézion, “irregular quadrilateral”, literally “a little table”) + -oid (“resembling”).

der

There was a trapezoid of light on his shoulder, some bright fragment torn from a greater plane.

2023, Brandon Taylor, The Late Americans, Jonathan Cape, page 178:

(geometry, US, Canada) A (convex) quadrilateral with two (non-adjacent) parallel sides.

trapezium

convex quadrilateral with two non-adjacent parallel sides

(geometry, British, Australia, New Zealand) A convex quadrilateral with no sides parallel.

irregular quadrilateral

convex quadrilateral with no parallel sides


hemisphere

hemispheres (plural)
hemisphære (alternative)

→ Welsh: hemisffer

From Latin hemisphaerium, from Ancient Greek ἡμισφαίριον (hēmisphaírion), from ἡμι- (hēmi-, “half”) + σφαῖρα (sphaîra, “sphere”). Equivalent to hemi- + sphere. Displaced native Old English healftrendel (literally “half-sphere”).

ncog

(geometry) Any half-sphere, formed by a plane intersecting the center of a sphere. .


compass

From Middle English compas (“a circle, circuit, limit, form, a mathematical instrument”), from Old French compas, from Medieval Latin compassus (“a circle, a circuit”), from Latin com- (“together”) + passus (“a pace, step, later a pass, way, route”); see pass, pace.

der

within the compass of an encircling wall

(obsolete) An enclosing limit; a boundary, a circumference.


skew

en-adj

skew (not generally comparable, comparative skewer or more skew, superlative skewest or most skew)

skewer (comparative)
more skew (comparative)
skewest (superlative)
most skew (superlative)

The verb is derived from Middle English skeuen, skewe, skewen (“to run at an angle or obliquely; to escape”), from Old Northern French escuer [and other forms], variants of Old French eschuer, eschever, eschiver (“to escape, flee; to avoid”) (modern French esquiver (“to dodge (a blow), duck; to elude, evade; to slip away; to sidestep”)), from Frankish *skiuhan (“to dread; to avoid, shun”), from Proto-Germanic *skiuhijaną (“to frighten”). The English word is cognate with Catalan esquiu (“evasive, shy”), Danish skæv (“crooked, slanting; skew, wry”) (> Norwegian Bokmål skjev), Dutch scheef (“crooked, slanting”), Norwegian skeiv (“crooked, lopsided; oblique, slanting; distorted”), Saterland Frisian skeeuw (“aslant, slanting; oblique; awry”), and is a doublet of eschew.
The adjective and adverb are probably derived from the verb and/or from askew, and the noun is derived from either the adjective or the verb.

cog

Through the given point there are two lines one of which is parallel to one of the given skew lines, while the other is parallel to the other of the given skew lines. These two "parallels" determine a plane, and the only plane, that is parallel to both the given skew lines.

1963, [George David] Birkhoff, [Ralph] Beatley, Basic Geometry: Answer Book, [New York, N.Y.]: Chelsea Publishing Company, →OCLC:

(not comparable, geometry) Of two lines in three-dimensional space: neither intersecting nor parallel.

vino

of two lines in three-dimensional space: neither intersecting nor parallel


irregular

en-adj

irregular (comparative more irregular, superlative most irregular)

more irregular (comparative)
most irregular (superlative)

/ɪˈɹɛɡ.jʊ.lə/

/ɪˈɹɛɡ.jə.lɚ/

From Middle English irreguler, from Old French irreguler, from Medieval Latin or Late Latin irrēgulāris, from in- + regularis, equivalent to ir- + regular.

(geometry, of a polygon) not regular; having sides that are not equal or angles that are not equal

(geometry, of a polyhedron) whose faces are not all regular polygons (or are not equally inclined to each other)


regular

regular (comparative more regular, superlative most regular)

more regular (comparative)
most regular (superlative)
reg'lar (alternative)
reg (alternative)
reg. (alternative)

/ˈɹɛɡ.jə.lɚ/

[ˈɹɛɡ.jɪ̈.lɚ]

From Middle English reguler, from Anglo-Norman reguler, Middle French reguler, regulier, and their source, Latin rēgulāris (“continuing rules for guidance”), from rēgula (“rule”), ultimately from Proto-Indo-European *reg- (“move in a straight line”).

register

not etymologically related but has semantic associations

(geometry, of a polygon) Both equilateral and equiangular; having all sides of the same length, and all (corresponding) angles of the same size

مُنْتَظِمٌ

of a polygon: having all sides and corresponding angles equal

(geometry, of a polyhedron) Whose faces are all congruent regular polygons, equally inclined to each other.

правилен

of a polyhedron: whose faces are all congruent regular polygons


quadrant

quadrants (plural)
quadraunt (alternative)

From Middle English quadrant, from Old French cadran, quadrant and its etymon Latin quadrāns, -antis (“fourth part of something, quarter”). Doublet of quadrans.

(geometry) One fourth of a circle or disc; a sector with an angle of 90°.


quadrilateral

Learned borrowing from Latin quadrilaterus.


angle

From Middle English angle, angul, angule, borrowed from Middle French angle, from Latin angulus, anglus (“corner, remote area”). Cognate with Old High German ancha (“nape of the neck”), Middle High German anke (“joint of the foot, nape of neck”). Doublet of angulus and ankle.

cog

the angle between lines A and B

(geometry) A figure formed by two rays which start from a common point (a plane angle) or by three planes that intersect (a solid angle).

The angle between lines A and B is π/4 radians, or 45 degrees.

The single-imaging optic of the mammalian eye offers some distinct visual advantages. Such lenses can take in photons from a wide range of angles, increasing light sensitivity. They also have high spatial resolution, resolving incoming images in minute detail.

2013 July-August, Fenella Saunders, “Tiny Lenses See the Big Picture”, in American Scientist:

(geometry) The measure of such a figure. In the case of a plane angle, this is the ratio (or proportional to the ratio) of the arc length to the radius of a section of a circle cut by the two rays, centered at their common point. In the case of a solid angle, this is the ratio of the surface area to the square of the radius of the section of a sphere.


ordinate

Borrowed from Latin ordino, ordinatus. Doublet of ordain.

(geometry) The second of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.

(geometry) The vertical line representing an axis of a Cartesian coordinate system, on which the ordinate (sense above) is shown.


right

en-adj

right (comparative further right or more right or righter, superlative furthest right or most right or rightmost or rightest)

further right (comparative)
more right (comparative)
righter (comparative)
furthest right (superlative)
most right (superlative)
rightmost (superlative)
rightest (superlative)
ryght (alternative)
reight (alternative)
rite (alternative)

→ Spanish: right

→ Welsh: reit

From Middle English right, from Old English riht, reht (“right,” also the word for “straight” and “direct”), from Proto-West Germanic *reht, from Proto-Germanic *rehtaz, from Proto-Indo-European *h₃reǵtós (“having moved in a straight line”), from *h₃reǵ- (“to straighten, direct”).
The Germanic adjective which has been used also as a noun since the common Germanic period. Cognate with West Frisian rjocht, Dutch recht, German recht and Recht, Swedish rätt and rät, Danish ret, Norwegian Bokmål rett, Norwegian Nynorsk rett, Yiddish רעכט (rekht) and Icelandic rétt. The Indo-European root is also the source of Ancient Greek ὀρεκτός (orektós) and Latin rēctus; Albanian drejt was borrowed from Latin.

inh

the left hand doesn't know what the right hand is doing

even a stopped clock is right twice a day

have one's head screwed on the right way

The kitchen counter formed a right angle with the back wall.

(geometry) Of an angle, having a size of 90 degrees, or one quarter of a complete rotation; the angle between two perpendicular lines.

a right triangle   a right prism   a right cone

(geometry) Of a geometric figure, incorporating a right angle between edges, faces, axes, etc.

перпендикулярен

geometry: incorporating a right angle between edges, faces, axes, etc.


project

en-verb

project (third-person singular simple present projects, present participle projecting, simple past and past participle projected)

projects (present singular third-person)
projecting (participle present)
projected (participle past)
projected (past)

/pɹəˈd͡ʒɛkt/

From Latin prōiectus, perfect passive participle of prōiciō (“throw forth, extend; expel”).

(geometry) To draw straight lines from a fixed point through every point of any body or figure, and let these fall upon a surface so as to form the points of a new figure.


lemon

en-noun

lemon (countable and uncountable, plural lemons)

desc

→ Kashubian: lemòna (Canada, United States)

Cream Lemon
Lemon
Lemon (color)
Lemon (geometry)

Inherited from Middle English lymon, from Old French lymon (“citrus”), from Arabic لَيْمُون (laymūn) or Persian لیمون (limon), from Persian لیمو (limu), from Sanskrit निम्बू (nimbū, “lime”), ultimately from Proto-Malayo-Polynesian *limaw or Munda. Likely doublet of lime.
The fandom sense is named after the erotic anime series Cream Lemon.

(geometry) The surface of revolution of a circular arc of angle less than 180° rotated about the straight line passing through the arc’s two endpoints.


scalene triangle

en-noun

scalene triangle (plural scalene triangles)

(geometry) A triangle having each of its three sides of different lengths.


pyramidal

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-pyramidal.wav

At one point was an isolated pyramidal rock, crowned by a great tree, which appeared to be separated by a cleft from the main crag.

1912, Arthur Conan Doyle, The Lost World […], London; New York, N.Y.: Hodder and Stoughton, →OCLC:

Below is the deep abyss of the Lauterbrunnen valley, and at its head a stately semi-circle of mountains, with the pyramidal Lauterbrunnen Breithorn as the centre-piece.

1960 December, Voyageur, “The Mountain Railways of the Bernese Oberland”, in Trains Illustrated, page 752:

Among its attractive features were decorative, tile-hung Italianate towers with pyramidal roofs.

2023 March 22, Dr Joseph Brennan, “Grand buildings on the list... and lost: Greenock Princes Pier”, in RAIL, number 979, page 52:

(geometry) Pyramid-shaped.
(crystallography) Tetragonal.


pyramidoid

pyramidoids (plural)
pyramoid (alternative)

/pɪˈɹæmɪdɔɪd/

(geometry) A solid resembling a pyramid.


pyramoid

LL-Q1860 (eng)-Flame, not lame-pyramoid.wav

(geometry) Alternative form of pyramidoid.


leg

→ Finnish: legi

→ Hungarian: leg

From Middle English leg, legge, from Old Norse leggr (“leg, calf, bone of the arm or leg, hollow tube, stalk”), from Proto-Germanic *lagjaz, *lagwijaz (“leg, thigh”) (see it for more).
Cognate with Scots leg (“leg”), Icelandic leggur (“leg, limb”), Norwegian Bokmål legg (“leg”), Norwegian Nynorsk legg (“leg”), Swedish lägg (“leg, shank, shaft”), Danish læg (“leg”), Lombardic lagi (“thigh, shank, leg”), Latin lacertus (“limb, arm”), Persian لنگ (leng). Upon borrowing, mostly displaced the native Old English term sċanca (Modern English shank).

der

don't pee on my leg and tell me it's raining

don't piss on my leg and tell me it's raining

piss on someone's leg and tell them it's raining

(geometry) One of the two sides of a right triangle that is not the hypotenuse.

been

(mathematics) leg (non-hypotenuse) of a right triangle

(geometry) One of the two equal sides of an isosceles triangle.

(geometry) One of the branches of a hyperbola or other curve which extend outward indefinitely.


foot

en-noun

foot (plural feet or (UK colloquial, unit of measure) foot)

feet (plural)
foot (plural)
foote (alternative obsolete)
feets (alternative dialectal)
foots (alternative nonstandard)

→ Assamese: ফুট (phut)

q

from <i class="Latn mention" lang="en">feet</i>

→ Japanese: フット (futto), フート (fūto); フィート (fīto) (from feet)

→ Russian: фут (fut)

Sranan Tongo: futu

Aukan: futu

Saramaccan: fútu

→ Swahili: futi

→ Thai: ฟุต (fút)

Tok Pisin: fut, put

→ Urdu: فٹ (fuṭ)

→ Phalura: fuṭ

From Middle English fot, fote, foot, from Old English fōt, from Proto-West Germanic *fōt, from Proto-Germanic *fōts, from Proto-Indo-European *pṓds. Doublet of pes, pie (“Spanish unit of length”), and pous.

doublet

not touch something with a ten-foot pole

you cannot put the same shoe on every foot

(geometry) The point of intersection of one line with another that is perpendicular to it.


face

Sranan Tongo: fesi

→ Danish: fjæs

→ Norwegian:

Norwegian Bokmål: fjes

Norwegian Nynorsk: fjes

→ Swedish: fejs, fjäs

→ Wu: 番斯 (¹fe-sy)

Etymology tree
Proto-Indo-European *dʰeh₁-?
Latin faciēs
Late Latin facia
Old French facebor.
Middle English face
English face
From Middle English face, from Old French face, from Late Latin facia, from Latin faciēs (“form, appearance”). Doublet of facies. Displaced native onlete (“face, countenance, appearance”), anleth (“face”), from Old English anwlite, andwlita, compare German Antlitz; Old English ansīen (“face”), Middle English neb (“face, nose”) (from Old English nebb), Middle English ler, leor, leer (“face, cheek, countenance”) (from Old English hlēor), and non-native Middle English vis (“face, appearance, look”) (from Old French vis) and Middle English chere (“face”) from Old French chere.
In the sense of face as in reputation, influenced by Chinese 面子 (miànzi) or 臉／脸 (liǎn), both of which mean literally the front of the head and metaphorically one's public image. See lose face.

noncog

talk to the hand 'cause the face ain't listening

A cube has six faces, each of which is a square.

facet

different specialised meaning in mathematical use

(geometry) Any of the flat bounding surfaces of a polyhedron; more generally, any of the bounding pieces of a polytope of any dimension.

kant

geometry: bounding surface of a polyhedron


dimension

(geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.


circle

Pitcairn-Norfolk: sirkil

From Middle English circle, cercle, from Old French cercle and Latin circulus, diminutive of Latin circus (“circle, circus”), from Ancient Greek κίρκος (kírkos, “circle, ring”), related to Old English hring (“ring”). Compare also Old English ċircul (“circle, zodiac”), which came from the same Latin source.

der

The set of all points (x, y) such that (x − 1)² + y² = r² is a circle of radius r around the point (1, 0).

(geometry) A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given point (center).

аикәагьежь

geometry: set of points that are equally distant from a center


body

en-noun

body (countable and uncountable, plural bodies)

bodies (plural)
bodie (alternative obsolete)

→ Bislama: bodi

→ Chichewa: bóde

→ Finnish: bodi

→ Indonesian: bodi

Jamaican Creole: badi, bady

Nigerian Pidgin: bọdí

→ Spanish: bodi

→ Swahili: bodi

desc

→ Thai: บอดี้ (bɔɔ-dîi), บอดี

→ Thai: บอดี้ (bɔɔ-dîi), บอดี

Tok Pisin: bodi

Torres Strait Creole: bodi

Etymology tree
Proto-Indo-European *bʰewdʰ-
Proto-West Germanic *bodag
Old English bodiġ
Middle English bodi
English body
From Middle English bodi, bodiȝ, from Old English bodiġ (“body, trunk, chest, torso, height, stature”), from Proto-West Germanic *bodag (“body, trunk”), from Proto-Indo-European *bʰewdʰ- (“to be awake, observe”). Cognate with Old High German botah (whence Swabian Bottich (“body, torso”)).

有黏性

comparative viscosity, solidity or substance

body-focused repetitive behavior disorder

(geometry) A three-dimensional object, such as a cube or cone.


complex

en-adj

complex (comparative more complex or (nonstandard) complexer, superlative most complex or (nonstandard) complexest)

more complex (comparative)
complexer (comparative nonstandard)
most complex (superlative)
complexest (nonstandard superlative)

From French complexe, from Latin complexus, past participle of complector (“I entwine, encircle, compass, infold”), from com- (“together”) and plectere (“to weave, braid”). May be analyzed as com- + -plex. See complect. Doublet of complexus.

(geometry) A curve, polygonderi or other figure that crosses or intersects itself.


branch

branches (plural)
braunch (alternative obsolete)

From Middle English branche, braunche, bronche, from Old French branche, branke, from Late Latin branca (“footprint”, later also “paw, claw”) (whence Middle High German pranke, German Pranke (“paw”)), of unknown origin.
Perhaps of Celtic origin, from a hypothetical Gaulish *vranca, from Proto-Indo-European *wrónk-eh₂. If so, then Indo-European cognates include Old Norse rá, vró (“angle, corner”), and possibly Lithuanian rankà (“hand”), Old Church Slavonic рѫка (rǫka, “hand”), Albanian rangë (“yardwork”).
The verb is from Middle English braunchen, from the noun.

unk

unknown

fall out of the ugly tree and hit every branch

the highest branch is not the safest roost

the branches of a hyperbola

(geometry) One of the portions of a curve that extends outwards to an indefinitely great distance.

haara

geometry: one of the portions of a curve that extends to infinity


curve

Attested since the 1690s, from Latin curvus (“bent, curved”), ultimately from Proto-Indo-European *(s)ker- (“to bend, curve, turn”) + *-wós. Doublet of curb, shrink, carcer, and cancer.

doublet

(analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.

(geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.


cell

From Middle English celle, selle, from Old English cell (attested in inflected forms), from Latin cella (“chamber, small room, compartment”), later reinforced by Old French cel, sele, Old French cele. ultimately from Proto-Italic *kelnā, from Proto-Indo-European *ḱelneh₂, from Proto-Indo-European *ḱel- (“to cover”). Doublet of cella and hall.

der

intrinsically photosensitive retinal ganglion cell

melanopsin-containing retinal ganglion cell

(geometry) A three-dimensional facet of a polytope.

포

geometry: a three-dimensional facet of a polytope


ring

→ French: ring
→ Romanian: ring

→ Hungarian: ring

→ Italian: ring

→ Japanese: リング

→ Polish: ring

→ Serbo-Croatian: ring

→ Spanish: ring

→ Turkish: ring

From Middle English ryng, from Old English hring (“ring, circle”), from Proto-West Germanic *hring, from Proto-Germanic *hringaz (“ring”), from Proto-Indo-European *(s)krengʰ-, extended nasalized form of *(s)ker- (“to turn, bend”). Doublet of rank and rink, as well as indirectly range.
Cognates
* West Frisian ring
* Low German Ring
* Dutch ring
* German Ring
* Swedish ring
* Finnish rengas
More distantly cognate with Proto-Slavic *krǫgъ (whence Bulgarian кръг (krǎg), Polish krąg, Russian круг (krug)).

(geometry) A planar geometrical figure included between two concentric circles.


spread

en-noun

spread (countable and uncountable, plural spreads)

From Middle English spreden, from Old English sprǣdan (“to spread, expand”), from Proto-Germanic *spraidijaną (“to spread”), from Proto-Indo-European *(s)per- (“to strew, sow, sprinkle”).
Cognate with Saterland Frisian spreede (“to spread”), West Frisian spriede (“to spread”), North Frisian spriedjen (“to spread”), Dutch spreiden (“to spread”), Low German spreden (“to spread”), German spreiten (“to spread, spread out”), Norwegian spre, spreie (“to spread, disseminate”), Swedish sprida (“to spread”), Latin spernō, spargō, Ancient Greek σπείρω (speírō), Persian سپردن (sepordan, “to deposit”), English spurn.

cog

(geometry) An unlimited expanse of discontinuous points.


tore

non-rhotic, without the horse–hoarse merger

(geometry) The surface described by the circumference of a circle revolving about a straight line in its own plane.


round

en-adj

round (comparative rounder or more round, superlative roundest or most round)

rounder (comparative)
more round (comparative)
roundest (superlative)
most round (superlative)
around (alternative)
ron (alternative)

From Middle English round, rounde, from Old Northern French roünt, rund, Old French ront, runt, reont ( > French rond), from both Late Latin retundus and the original Latin rotundus. The noun developed partly from the adjective and partly from the corresponding French noun rond. Doublet of rotund.

pyöreä

pronounced with the mouth in the shape of an "O"

The ancient Egyptian demonstrated that the Earth is round, not flat.

Spherical; shaped like a ball; having a circular cross-section in more than one direction.


box

en-noun

box (plural boxes or (nonstandard, computing, humorous) boxen)

boxes (plural)
boxen (humorous nonstandard plural)

Tok Pisin: bokis

→ Afrikaans: boks

→ Bengali: বাক্স (bakśo)

→ Bulgarian: бокс (boks)

→ Crimean Tatar: boks

→ Danish: boks

→ Dutch: box m

→ Faroese: boks

→ French: box m

→ German: Box f

→ Hindustani:

Hindi: बकस m (bakas), बक्सा m (baksā)

Urdu: بکس m (baks, bakas)

→ Icelandic: box n

→ Indonesian: boks

→ Irish: bosca m

→ Italian: box m

→ Japanese: ボックス (bokkusu)

→ Korean: 박스 (bakseu)

→ Maori: pāka

→ Marwari: बकस (baks, bakas)

→ Nepali: बाकस (bākas)

→ Norman: bosc m

→ Norwegian: boks m

→ Pashto: بکس (baks)

→ Persian: باکس (bâks)

→ Polish: boks m

→ Portuguese: box m

→ Russian: бокс m (boks)

→ Scottish Gaelic: bogsa m, bocsa

→ Spanish: box m

→ Swedish: box c

→ Welsh: bocs

Etymology tree
Ancient Greek πῠ́ξος (pŭ́xos)
Ancient Greek -ις (-is)
Ancient Greek πυξίς (puxís)bor.
Late Latin buxisbor.
Proto-West Germanic *buhsā
Old English box
Middle English box
English box
From Middle English box (“container, box, cup”), from Old English box (“box, case”), from Proto-West Germanic *buhsā (“box”) from Late Latin buxis (“box”), Latin pyxis (“small box for medicines or toiletries”), of uncertain origin; compare Ancient Greek πύξος (púxos, “box or tablet made of boxwood; box; cylinder”) and Ancient Greek πυξίς (puxís, “box or tablet made of boxwood; box; cylinder”). Doublet of piseog, pyx, and pyxis.
Cognate with Middle Dutch bosse, busse (“jar; tin; round box”) (modern Dutch bos (“wood, forest”), bus (“container, box; bushing of a wheel”)), Old High German buhsa (Middle High German buhse, bühse, modern German Büchse (“box; can”)), Swedish bössa (“box”).
The humorous plural form boxen is from box + -en, by analogy with oxen.

кутия

compartment or receptacle for receiving items

ramme

rectangular border around an image, text, etc.

квадратче

small area on a document for a tick mark

tofu

empty box displayed by some computer systems in place of a character not supported by available fonts

(geometry, by extension) A rectangular object in any number of dimensions.


base

en-noun

base (countable and uncountable, plural bases)

acid

antonym(s) of “chemical compound that will neutralize an alkali”

From Middle English base, bas, baas, from Old French base, from Latin basis, from Ancient Greek βάσις (básis). Doublet of basis and bass.

أَسَاس

something from which other things extend

basis

chemical compound that will neutralize an acid

(geometry) The lowest side of a triangle or other polygon, or the lowest face of a cone, pyramid or other polyhedron laid flat.

భూమి

త్రిభుజం వైశాల్యం = అర*భూమి*ఎత్తు


altitude

altitude (countable and uncountable, plural altitudes)

From Middle English, borrowed from Latin altitūdō (“height”), from altus (“high”).

The perpendicular height of a triangle is known as its altitude.

(geometry) The distance measured perpendicularly from a figure's vertex to the opposite side of the vertex.


flat

From Middle English flat, a borrowing from Old Norse flatr (compare Norwegian and Swedish flat, Danish flad), from Proto-Germanic *flataz, from Proto-Indo-European *pleth₂- (“flat”); akin to Saterland Frisian flot (“smooth”), German Flöz (“a geological layer”), Ancient Greek πλατύς (platús), Latvian plats, Sanskrit प्रथस् (prathas, “extension”). Doublet of plat and pleyt.
The noun is from Middle English flat (“level piece of ground, flat edge of a weapon”), from the adjective.
The algebraic sense was coined by Serre in a 1956 paper, originally as French plat.

inh

(geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.


apex

Borrowed from Latin apex (“point, tip, summit”).

The highest or the greatest part of something, especially forming a point.

(geometry) The highest point in a plane or solid figure, relative to a base line or plane.


solid

From Middle English solid, from the adjective, Middle French solide, or Latin solidum. Doublet of solidum.

(geometry) A three-dimensional figure (as opposed to a surface, an area, or a curve).


space

en-noun

space (countable and uncountable, plural spaces)

From Middle English space, from Anglo-Norman space, variant of espace, espas et al., and spaze, variant of espace, from Latin spatium, from Proto-Indo-European *(s)peh₂- (“to stretch, to pull”).

مَسَافَة

gap between written characters, lines etc.

Fully Automated Luxury Queer Space Communism

(heading) A bounded or specific extent, physical or otherwise.

(geometry) A set of points, each of which is uniquely specified by a number (the dimensionality) of coordinates.


volume

en-noun

volume (countable and uncountable, plural volumes)

volumes (plural)
vol. (alternative abbreviation)

From Middle English volume, from Old French volume, from Latin volūmen (“book, roll”), from volvō (“roll, turn about”).

(obsolete) A roll or scroll, which was the form of ancient books.

сви́тък

The volume of ticket sales decreased this week.

ծավալ

synonym for quantity — see also quantity

(computing) An accessible storage area with a single file system, typically resident on a single partition of a hard disk.

том

computing: accessible storage area with a single file system

(climbing, bouldering) A modular foothold attached to a climbing wall used for gripping, often in triangular, pyramidal, or angular shapes.


crown

→ Japanese: クラウン (kuraun)

→ Korean: 크라운 (keuraun)

→ Maori: karauna

From Middle English coroune, from Anglo-Norman corone, from Latin corōna (“crown, wreath”), from Ancient Greek κορώνη (korṓnē). Doublet of corona, korona, koruna, krona, króna, and krone. Displaced native Old English corenbēag (“crown”); and Middle English kinehelm, kynehelm, from Old English cynehelm (“crown”).
* (paper size): So called because originally watermarked with a crown.

doublet

(geometry) The area enclosed between two concentric perimeters.

rengas

geometry: area enclosed between two concentric perimeters


orbit

en-noun

orbit (countable and uncountable, plural orbits)

Inherited from Middle English orbite, orbita, from Latin orbita (“course, track, impression, mark”).

គន្លង

kɔɔkŭənlɔɔng

(geometry, group theory) The subset of elements of a set X to which a given element can be moved by members of a specified group of transformations that act on X.


right angle

(geometry) Half of the angle formed by a single straight line, equivalent to 90 degrees.


wedge

en-noun

wedge (countable and uncountable, plural wedges)

From Middle English wegge (“wedge”), from Old English weċġ (“wedge”), from Proto-West Germanic *wagi, from Proto-Germanic *wagjaz.

(geometry) A five-sided polyhedron with a rectangular base, two rectangular or trapezoidal sides meeting in an edge, and two triangular ends.


cylinder

→ Japanese: シリンダー (shirindā)

→ Korean: 실린더 (sillindeo)

From Middle French chilindre, cylindre, from Latin cylindrus, from Ancient Greek κύλινδρος (kúlindros), from κυλίνδω (kulíndō) "I roll or wallow" (intransitive). Doublet of calander and calender.

When the two-dimensional curve is a circle, the cylinder is called a circular cylinder. When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. In non-mathematical usage, both right and circular are usually implied.

(geometry) A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

(geometry) A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder.


x-axis

independent variable
independent variable

(analytic geometry) The axis on a graph that is usually drawn left to right and usually shows the range of values of an independent variable.


hyperbola

hyperbola (plural hyperbolas or hyperbolae or hyperbolæ)

hyperbolas (plural)
hyperbolae (plural)
hyperbolæ (plural)

From New Latin hyperbola, from Ancient Greek ὑπερβολή (huperbolḗ). Doublet of hyperbole.

(geometry) A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone. The function y(x) = 1/x draws a hyperbola.


similarity

similarity (countable and uncountable, plural similarities)

From French similarité.
Morphologically similar + -ity

(geometry) A transformation (of a Euclidean space) that preserves angles and the ratios of distances


aberrancy

aberrancy (countable and uncountable, plural aberrancies)

LL-Q1860 (eng)-Flame, not lame-aberrancy.wav

(geometry) The deviation of a curve from circular form.


generation

generation (countable and uncountable, plural generations)

/ˌd͡ʒɛnəˈɹeɪʃən/

Inherited from Middle English generacioun, from Anglo-Norman generacioun, Middle French generacion, and their source, Latin generātiō, from generāre (“to beget, generate”). By surface analysis, generate + -ion.

inh+

the generation of a line or curve

(geometry) The formation or production of any geometrical magnitude, as a line, a surface, a solid, by the motion, in accordance with a mathematical law, of a point or a magnitude, by the motion of a point, of a surface by a line, a sphere by a semicircle, etc.


group

groups (plural)
groop (alternative nonstandard)
groupe (alternative obsolete)

→ Gulf Arabic: قروب (grūp)

→ Japanese: グループ (gurūpu)

→ Korean: 그룹 (geurup)

→ Tongan: kulupu

From French groupe (“cluster, group”), from Italian gruppo, groppo (“a knot, heap, group, bag (of money)”), from Vulgar Latin *cruppo, Renaissance Latin grupus, from Frankish *krupp, from Proto-Germanic *kruppaz (“lump, round mass, body, crop”), from Proto-Indo-European *grewb- (“to crumple, bend, crawl”).
In the “group theory” sense, calqued from French groupe, a term coined by the young French mathematician Évariste Galois in 1830.
Cognate with German Kropf (“crop, craw, bunch”); Old English cropp, croppa (“cluster, bunch, sprout, flower, berry, ear of corn, crop”) (whence English crop); Dutch krop (“craw”), Icelandic kroppr (“hump, bunch”). Doublet of crop and croup.

der

(geometry, archaic) An effective divisor on a curve.


essential

en-adj

essential (comparative more essential, superlative most essential)

more essential (comparative)
most essential (superlative)
essentiall (alternative)

From Late Latin essentiālis, from Latin essentia (“being, essence”).

complementary region
complementary region

(geometry) Such that each complementary region is irreducible, the boundary of each complementary region is incompressible by disks and monogons in the complementary region, and no leaf is a sphere or a torus bounding a solid torus in the manifold.


lune

What he worried about was any eventual convexity, a shrinking, it might be, of the planet itself to some palpable curvature of whatever he would be standing on, so that he would be left sticking out like a projected radius, unsheltered and reeling across the empty lunes of his tiny sphere.

(geometry) A concave figure formed by the intersection of the arcs of two circles on a plane, or on a sphere the intersection between two great semicircles.


trigonometry

en-noun

trigonometry (countable and uncountable, plural trigonometries)

/ˌtɹɪɡəˈnɒmətɹi/

PIE word
 *tréyes
From 1610s, from New Latin trigōnometria, from Ancient Greek τρίγωνον (trígōnon, “triangle”) + μέτρον (métron, “measure”), equivalent to trigono- + -metry.

EtymOnLine

Douglas Harper (2001–2025) “trigonometry”, in Online Etymology Dictionary.

Trigonometry emerged in the Hellenistic world during the 3rd century BCE from applications of geometry to astronomy; the Greeks focused on the calculation of chords, while mathematicians in India created the earliest known tables of values for trigonometric functions such as sine.

Historically, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics and navigation.

Trigonometry was originally the science which treated only of the sides and angles of plane and spherical triangles; but it has been recently extended so as to include the analytic treatment of all theorems involving the consideration of angular magnitudes.

1892, Edward Albert Bowser, A Treatise on Plane and Spherical Trigonometry, D. C. Heath & Co., page 1:

In fact, the earliest practical uses of trigonometry were in the fields of astronomy and hence navigation.

2013, Paul Abbott, Hugh Neill, Trigonometry: A Complete Introduction, Hachette, unnumbered page:

The properties of these new trigonometries and identities flowing from the definitions are then developed.
The trigonometries derived from these generalizations will be jointly termed "The Fractional Trigonometry."

2016, Carl F. Lorenzo, Tom T. Hartley, The Fractional Trigonometry, Wiley, page 8:

mathematical analysis
mathematical analysis

right-angled triangle
right-angled triangle

trigonometric function
trigonometric function

(geometry, mathematical analysis) The branch of mathematics that deals with the relationships between the sides and angles of (in particular) right-angled triangles, as represented by the trigonometric functions, and with calculations based on said relationships.


cubic

From Middle French cubique, equivalent to cube + -ic.

cubic foot

On one recent day, officials said the fine dust concentration levels in Seoul rose above 130 micrograms per cubic meter.

2019, VOA Learning English (public domain)

(geometry) Used in the names of units of volume formed by multiplying a unit of length by itself twice.


line

→ Scottish Gaelic: loidhne

From Middle English line, lyne, from Old English līne (“line, cable, rope, hawser, series, row, rule, direction”), from Proto-West Germanic *līnā, from Proto-Germanic *līnǭ (“line, rope, flaxen cord, thread”), from Proto-Germanic *līną (“flax, linen”), from Proto-Indo-European *līno- (“flax”).
Influenced in Middle English by Middle French ligne (“line”), from Latin linea. More at linen.
The oldest sense of the word is “rope, cord, thread”; from this the senses “path”, “continuous mark” were derived.

lyn

path through two or more points, threadlike mark

lyn

single horizontal row of text on a screen, printed paper, etc.

linja

measure of length, the main division of an inch or its local equivalent

A path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight.

(geometry) An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness.

lyn

geometry: infinite one-dimensional figure

(geometry, informal) A line segment; a continuous finite segment of such a figure.

отсе́чка

geometry: continuous finite segment of such a figure


sphere

spheres (plural)
sphære (alternative archaic)
sphear (alternative archaic)
spheare (alternative obsolete)

From Middle English spere, from Old French sphere, from Late Latin sphēra, earlier Latin sphaera (“ball, globe, celestial sphere”), from Ancient Greek σφαῖρα (sphaîra, “ball, globe”), of unknown origin. Not related to superficially similar Persian سپهر (sepehr, “sky”) .

uder

(geometry) The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .

sferë

mathematics: regular three-dimensional object


polyhedron

en-noun

polyhedron (plural polyhedra or polyhedrons)

polyhedra (plural)
polyhedrons (plural)
polyedron (alternative)

From New Latin polyedron, from Ancient Greek πολύεδρος (polúedros, “having many seats”), from πολυ- (polu-, “many”) + ἕδρα (hédra, “seat”); compare French polyèdre. By surface analysis, poly- + -hedron.

der

quasiregular polyhedronArchimedean solidCatalan solid

regular polyhedronKepler-Poinsot polyhedronPlatonic solidcube

semiregular polyhedronantiprismArchimedean solidCatalan soliddipyramidprismtrapezohedron

List of uniform polyhedra on Wikipedia.Wikipedia

Of the convex polyhedra with regular faces, the only ones that have tetrahedral, octahedral, or icosahedral symmetry are the Platonic and Archimedean solids.

1966, Norman W. Johnson, “Convex Polyhedra with Regular Faces”, in Canadian Journal of Mathematics, volume XVIII, number I, Toronto: University of Toronto Press, page 181:

(geometry) A solid figure with many flat faces and straight edges.


decagram

decagrams (plural)
decagramme (UK) (alternative)
deca-gramme (alternative)
deca-gram (alternative)
dekagram (alternative)
deka-gram (alternative)
dekagramme (alternative)
deka-gramme (alternative)

LL-Q1860 (eng)-Flame, not lame-decagram.wav

(geometry) A regular ten-pointed star shape.


generator

/ˈdʒɛnəɹeɪtə(ɹ)/

From Latin, from past participle of genero (“beget, father”), equivalent to generate + -or.

One who, or that which, generates, begets, causes, or produces.

(geometry) One of the lines of a ruled surface; more generally, an element of some family of linear spaces.


generatrix

en-noun

generatrix (plural generatrices or generatrixes)

generatrices (plural)
generatrixes (plural)

LL-Q1860 (eng)-Flame, not lame-generatrix.wav

Learned borrowing from Latin generātrīx. By surface analysis, generator + -trix.

(geometry) A curve that, when rotated about an axis, produces a solid figure.

generatriu

a curve that, when rotated about an axis, produces a solid figure


generic

en-adj

generic (comparative more generic, superlative most generic)

more generic (comparative)
most generic (superlative)
generick (alternative obsolete)

gendered

antonym(s) of “neither masculine nor feminine”

/d͡ʒɪˈnɛɹɪk/

From Middle French générique, from Latin genus (“genus, kind”) + -ic; thus morphologically parallel with, and a doublet of, general.

(geometry, of a point) Having coordinates that are algebraically independent over the base field.


degree

→ Burmese: ဒီဂရီ (diga.ri)

→ Juba Arabic: digrii

→ Swahili: digrii

→ Tagalog: digri

From Middle English degre, borrowed from Old French degré (French: degré), itself from Latin gradus, with the prefix de-.

Appendix:Roget MICRA thesaurus/Class I § 26. Degree

Appendix:Roget MICRA thesaurus/Class I § 31. Greatness

Appendix:Roget MICRA thesaurus/Class I § 32. Smallness

A right angle is a ninety-degree angle.

Most humans have a field of vision of almost 180 degrees.

(geometry) A unit of measurement of angle equal to ¹⁄₃₆₀ of a circle's circumference.


plane

→ Irish: plána

From Latin plānum (“flat surface”), a noun use of the neuter of plānus (“plain”). The word was introduced in the 17th century to distinguish the geometrical senses from the other senses of plain. Doublet of llano, piano, and plain.

հարթություն

geometry: flat surface extending infinitely in all directions

Mirrors in the compartments have been canted out of the vertical plane to reduce reflections to the passengers when seated.

1979 August, Graham Burtenshaw, Michael S. Welch, “O.V.S. Bulleid's SR loco-hauled coaches - 1”, in Railway World, page 396:

(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane); a bounded portion thereof.

(anatomy) An imaginary plane which divides the body into two portions.


net

Etymology tree
Proto-Indo-European *neHd-
Proto-Indo-European *-yós
Proto-Germanic *natją
Proto-West Germanic *nati
Old English nett
Middle English net
English net
From Middle English net, from Old English net, nett, from Proto-West Germanic *nati, from Proto-Germanic *natją, from Proto-Indo-European *ned- (“to turn, twist, knot”).
Cognate with West Frisian net, Low German Nett, Dutch net, German Netz, Danish net, Swedish nät.

der

(geometry) Any set of polygons joined edge to edge that, when folded along the edges between adjoining polygons so that the outer edges touch, form a given polyhedron.


homogeneous

From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

abstract algebra
abstract algebra#English

(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).

(geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).

homogeneous coordinate
homogeneous coordinate

(geometry) Of or relating to homogeneous coordinates.


center

centers (plural)
centre (alternative Australia Canada Commonwealth Ireland New-Zealand South-Africa UK including usually)

From Middle English center, centre, from Middle French centre, from Latin centrum, from Ancient Greek κέντρον (kéntron), from κεντεῖν (kenteîn, “to prick, goad”). Doublet of centrum.
* (group theory): In the notation Z(G), the letter Z derives from the German Zentrum (“center”).

sentrum

point equidistant from all points on the perimeter of a circle

مَرْكَز

point in the interior of figure with mean coordinates

(geometry) The point on a line that is midway between the ends.

(geometry) The point in the interior of any figure of any number of dimensions that has as its coordinates the arithmetic mean of the coordinates of all points on the perimeter of the figure (or of all points in the interior for a center of volume).


intersection

/ˈɪntəɹˌsɛkʃən/

/ˌɪntəɹˈsɛkʃən/

From Middle French intersection and its etymon Latin intersectiō. By surface analysis, intersect + -ion.

(geometry) The point or set of points common to two geometrical objects (such as the point where two lines meet or the line where two planes intersect).


rectangle

/ˈrɛktæŋɡl̩/

Borrowed from Middle French, from Old French, from Medieval Latin or Late Latin rectangulum (“right angle”), from Latin rectus (“right”) + angulus (“an angle”).

(geometry) Any quadrilateral having opposing sides parallel and four right angles.


tangent

Borrowed from Latin tangentem, the accusative of tangēns (“touching”) (in the phrase līnea tangēns (“a touching line”)), the present participle of the verb tangō (“touch”, verb), from Proto-Italic *tangō, from Proto-Indo-European *teh₂g- (“to touch”).
Cognate with Old English þaccian (“to touch lightly, pat, stroke”). More at thack, thwack.

cog

(geometry) Touching a curve at a single point but not crossing it at that point.


dodecahedron

en-noun

dodecahedron (plural dodecahedra or dodecahedrons)

dodecahedra (plural)
dodecahedrons (plural)

From Ancient Greek δωδεκάεδρον (dōdekáedron). Equivalent to dodeca- + -hedron.

1707, Thomas Blount, Glossographia Anglicana Nova: Or, A Dictionary, Interpreting Such Hard Words, D. Brown, heading DO–DO,
Dodecahedron, (Gr.) in Geometry, is a solid Figure of 12 Sides or Faces that are regular Pentagons, it is one of the Platonick or Regular Bodies.

(geometry) A polyhedron with twelve faces; the regular dodecahedron has regular pentagons as faces and is one of the Platonic solids.


torus

Borrowed from Latin torus (“a round, swelling, elevation, protuberance”).

bor

A 4-variable Karnaugh map can be thought of, topologically, as being a torus.

(geometry) The standard representation of such a space in 3-dimensional Euclidean space: a surface or solid formed by rotating a closed curve, especially a circle, about a line which lies in the same plane but does not intersect it (e.g. like a ring doughnut).

(topology) A topological space which is a product of two circles.

(topology, in combination, n-torus, 4-torus, etc.) The product of the specified number of circles.

A ring-shaped object, especially a large ring-shaped chamber used in physical research.


obtuse

en-adj

obtuse (comparative obtuser or more obtuse, superlative obtusest or most obtuse)

obtuser (comparative)
more obtuse (comparative)
obtusest (superlative)
most obtuse (superlative)

clear

antonym(s) of “deadened, muffled, muted”

pointed

antonym(s) of “now chiefly botany, zoology”

From Middle English obtuse, from Latin obtūsus (“blunt, dull; obtuse”), past participle of obtundere, from obtundō (“to batter, beat, strike; to blunt, dull”), from ob- (“against”) (see ob-) + tundō (“to beat, strike; to bruise, crush, pound”) (ultimately from Proto-Indo-European *(s)tewd-, from *(s)tew- (“to hit; to push”)). More at obtund.

If you put foure Spleets in a Hiue, then cut their backes, where they must leane one against another, to square angles, such as be foure in a circle: if but three, cut them to obtuse angles, such as are three in a circle: (you may readily try them, before you put them in, by Moulds made iust to those formes) and so will they stand close and firme together.

1623, Charles Butler, “Of the Hiues, and the Dressing of Them”, in The Feminine Monarchie: or, The Historie of Bees: Shewing Their Admirable Nature, and Properties, Their Generation, and Colonies, Their Gouernment, Loyaltie, Art, Industrie, Enemies, Warres, Magnanimitie, &c. […], London, →OCLC, chapter 3, section 11, footnote c; republished Mytholmroyd, U.K.: Northern Bee Books, 1985:

More-over, as the Buildings Ambligon / May more receive then Mansions Oxigon / (Because th' acute, and the rect-Angles too, / Stride not so wide as obtuse Angles doe) / So doth the Circle in his Circuit span / More room then any other Figure can.

1641, “The Columnes. The Fourth Part of the Second Day of the II. Weeke”, in Alexander B. Grosart, editor, The Complete Works of Joshua Sylvester: For the First Time Collected and Edited […], Edinburgh Univ. Press, published 1880, page 156, lines 198–203:

Obtuse angles of the through crossing. — The system of the two obtuse-angled points is especially termed the dead-crossing. […] The point itself, less liable to damage than that of the crossing proper, on account of its obtuse form and its position relatively to the wheels, acts the same part towards the tapered portion of the cut rail, as the wing-rail does with respect to the acute-angle of the crossing.

1877, Ch[arles] Couche, “Special Points in the Permanent Way”, in James N. Shoolbred, transl., Permanent Way Rolling Stock and Technical Working of Railways. Followed by an Appendix on Works of Art, volume I, London: Dulau & Co., 37, Soho Square; Paris: Dunod, 49, Quai des Augustins, →OCLC, § XIV (Rail-crossings), paragraph 258, page 316:

If he is standing close beside me I know that our separate axes of vision will meet at an acute angle in the centre of his object, and if we are further apart, at an obtuser angle.

1922, May Sinclair, “Space, Time and Other Consciousnesses”, in The New Idealism, New York, N.Y.: The Macmillan Company, →OCLC, section V, pages 255–256:

(now chiefly botany, zoology) Blunt; not sharp, pointed, or acute in form.

(geometry, specifically, of an angle) Larger than one, and smaller than two right angles, or more than 90° and less than 180°.

բութ

geometry: larger than 90° but less than 180°

Unless A lies in that part of a semi-infinite strip bounded by AB outside a semi-circle of diameter AB, the triangle is obtuse, so that the probability of getting an obtuse triangle is equal to 1.

2013, Edward J. Barbeau, “Probability and Statistics”, in More Fallacies, Flaws, and Flimflam (Spectrum Series), Washington, D.C.: Mathematical Association of America, →ISBN, page 128:

(geometry, by ellipsis) Obtuse-angled, having an obtuse angle.


acute

acute (comparative acuter or more acute, superlative acutest or most acute)

acuter (comparative)
more acute (comparative)
acutest (superlative)
most acute (superlative)

From Late Middle English acute (“of a disease or fever: starting suddenly and lasting for a short time; of a humour: irritating, sharp”), from Latin acūta, from acūtus (“sharp, sharpened”), perfect passive participle of acuō (“to make pointed, sharpen, whet”), from acus (“needle, pin”). The word is cognate to ague (“acute, intermittent fever”).
As regards the noun, which is derived from the verb, compare Middle English acūte (“severe but short-lived fever; of blood: corrosiveness, sharpness; musical note of high pitch”).

cog

The teacher pointed out the acute angle.

Chlorophosphuret of nitrogen (at ordinary temperatures) is a solid crystalline body. […] The form of the crystals, as obtained by sublimation, is that of a rhomboid, of which the obtuse angle measures 131° or 132°, the acute 48° or 49°: the acute angle of this rhomboid, either at one or both ends, is often truncated, when of course the angle formed is about 114°: the hexagonal prism is also found.

1850 March 30, J[ohn] H[all] Gladstone, “On Chlorophosphuret of Nitrogen and Its Products of Decomposition”, in Henry Watts, editor, The Quarterly Journal of the Chemical Society of London, volume III, number X, London: Hippolyte Bailliere, […], published 1851, →OCLC, part I, page 138:

(geometry, of an angle) Less than 90 degrees.

حَادّ

(geometry) of an angle: less than 90 degrees

an acute triangle

In order to be an acute triangle, all three angles of a triangle must be less than 90°. These triangles can have very prickly personalities. So, if you want to create images of porcupines, rugged mountains, or narrow pine trees in your geometric design, you may best do it by using acute triangles[…]. The most commonly used acute triangle in quiltmaking is the equilateral triangle[…]. All three of its angles are 60°.

1997, Joen Wolfrom, “The Fascination of Shapes”, in The Visual Dance: Creating Spectacular Quilts, Lafayette, Calif.: C&T Publishing, →ISBN; republished Lafayette, Calif.: C&T Publishing, 2009, →ISBN, page 39:

(geometry, of a triangle) Having all three interior angles measuring less than 90 degrees.


complementary angle

en-noun

complementary angle (plural complementary angles)

Angle A is 40°, and its complementary angle, B, is 50°.

(geometry) An angle that, when added to another referenced angle, produces a right angle.


pyramid

pyramid (countable and uncountable, plural pyramids)

pyramids (plural)
piramis (alternative obsolete)
pyramis (alternative obsolete)

From French pyramide, from Old French piramide, from Latin pȳramis, pȳramidis, from Ancient Greek πῡραμίς (pūramís), possibly from πῡρός (pūrós, “wheat”) + ἀμάω (amáō, “reap”) or from Egyptian pr-m-ws (“height of a pyramid”), from pr (“(one that) comes forth”) + m (“from”) + ws (“height”). Schenkel and K. Lang proposed hypothetical Coptic *ⲡⲓⲣⲁⲙ (*piram) or *ⲫⲣⲁⲙ (*phram) derived from Egyptian mr via metathesis as a source of πῡραμίς (pūramís) while Schenkel also suggested it being the source of Arabic هرم although the latter is considered far-fetched by Takacs.

der

(geometry) A solid with triangular lateral faces and a polygonal (often square or rectangular) base.

piramidë

in geometry, a solid with triangular lateral faces and a polygonal base


rectangular

en-adj

rectangular (not generally comparable, comparative more rectangular, superlative most rectangular)

more rectangular (comparative)
most rectangular (superlative)

/ɹɛkˈtæŋɡjəlɚ/

/ɹɛkˈtæŋɡjʊlə/


pole

From Middle French pole, pôle, from Latin polus, from Ancient Greek πόλος (pólos, “axis of rotation”).

der

poll (one pronunciation or with the doll–dole merger)

(geometry) A fixed point relative to other points or lines.


radian

International System of Units
International System of Units

(geometry) In the International System of Units, the derived unit of plane angle: the angle subtended at the centre of a circle by an arc of its circumference equal in length to the radius of the circle. Symbol: rad.


steradian

LL-Q1860 (eng)-Flame, not lame-steradian.wav

(geometry) In the International System of Units, the derived unit of solid angle; the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere that has area r². Symbol: sr


radius

Borrowed from Latin radius (“ray”). Doublet of ray.

Fatima claims to have visited all the bars within a five-mile radius of her Manhattan apartment.

We start with spherical geometries. The two geometries on spheres of radiuses R₁ and R₂ are obviously identical if R₁ = R₂; moreover, the converse also holds.

1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:

The velocity dispersions of early- and late-type galaxies in compact groups change little with groupcentric radius; the radii sampled are less than 100~h#123;-1#125; kpc, smaller than the radii typically sampled by members of massive clusters of galaxies.

2016, Jubee Sohn, Ho Seong Hwang, Margaret J. Geller, Antonaldo Diaferio, Kenneth J. Rines, Myung Gyoon Lee, Gwang-Ho Lee, “Compact Groups of Galaxies with Complete Spectroscopic Redshifts in the Local Universe”, in JKAS, volume 2015:

(geometry) A line segment between any point of a circle or sphere and its center.

This contribution reduces with increasing distance p from the emitting surface element dA, due to conservation of energy, as the wave energy distributed across the spherical wave front remains constant, while the radius increases during ...

1998, Dieter Schuocker, Handbook of the Eurolaser Academy, Springer Science & Business Media, →ISBN, page 51:

(geometry) The length of this line segment.

полупре́чник m (polupréčnik, literally “semidiameter”)


analogy

en-noun

analogy (countable and uncountable, plural analogies)

/əˈnæləd͡ʒi/

From Latin analogia, from Ancient Greek ἀναλογίᾱ (analogíā), from ἀνα- (ana-) + λόγος (lógos, “speech, reckoning”).

(geometry) The proportion or the equality of ratios.


turn

→ Japanese: ターン (tān)

Partly from Anglo-Norman *torn, from Latin tornus, from Ancient Greek τόρνος (tórnos), and partly an action noun from the verb turn.

دَوْرَة

movement about an axis ending up with the same orientation

360° turn

movement about an axis returning to the original orientation

the first turn of the screw pays all debts

A movement of an object about its own axis in one direction that continues until the object returns to its initial orientation.

(geometry) A unit of plane angle measurement based on this movement.

kierros

geometry: unit of plane angle measurement based on this movement


cylindrical

en-adj

cylindrical (comparative more cylindrical, superlative most cylindrical)

more cylindrical (comparative)
most cylindrical (superlative)

From Latin cylindricus + -al. By surface analysis, cylinder + -ical.


hexagon

From Latin hexagōnum, from Ancient Greek ἑξάγωνον (hexágōnon). By surface analysis, hexa- + -gon.

The project was a huge, queen-size quilt made up of 100 hexagon pieces – 50 of them embroidered with a design for every US state and 50 stars. […] Once the designs are all stitched and the hexagons are returned to Downey, they will be assembled into the completed quilt.

2019 October 25, Konstantin Toropin, “A woman found an unfinished, 20-year-old quilt and complete strangers are helping piece it together”, in CNN:

If we just plopped down a dot for every observation we’d end up with an undifferentiated black blob, so the weathergami technique visualizes frequency of temperature pairs: we divide the chart area into a fine hexagonal grid, and then color each hexagon according to how many daily observations fall within it.

2023 November 9, Christopher Ingram, ““Weathergami” charts paint new portrait of Minnesota climate”, in Minnesota Reformer:

(geometry) A polygon with six sides and six angles.


octagon

octagons (plural)
octogon (alternative obsolete)

From Latin octagōnon, octōgōnon (“octagon”), and from its etymon Ancient Greek ὀκτάγωνον (oktágōnon, “octagon”), probably from Koine Greek ὀκτάγωνος (oktágōnos, “having eight corners”) + -ον (-on, suffix forming nouns). ὀκτάγωνος is derived from ὀκτᾰ- (oktă-, prefix meaning ‘eight’) (from ὀκτώ (oktṓ, “eight”), ultimately from Proto-Indo-European *oḱtṓw (“eight”)) + γωνία (gōnía, “angle; corner”) (probably ultimately from Proto-Indo-European *ǵónu (“knee”)); analysable as octa- + -gon. The English word is cognate with Middle French octogone (modern French octogone), Italian octagono (obsolete), ottagono, Spanish octágono, octógono.
Sense 2 (“arena for mixed martial arts”) refers to its shape.

der

From the Circle deſcribe the Octagon, by taking half the Quadrant of the former for each Side of the latter. [...] [B]y conjoining theſe Points with ſtrait Lines agreeable to the Shape of the Octagon, the whole Work is completed.

1707, Andrea Pozzo, “The Ninety-second Fig. An Octangular Cupola.”, in John James, transl., Rules and Examples of Perspective Proper for Painters and Architects, etc. in English and Latin: […], London: […] Benj[amin] Motte [Sr.], […]; [s]old by John Sturt […], →OCLC:

In like manner it is demonſtrated that one angle of a regular hexagon will be equal to one right angle, and one third part of one right angle; one angle of a regular octagon equal to one right angle and half a right angle; [...]

1752, Euclid, “[Additions to the Fourth Book.] Prop[osition] VII. Probl[em]. To Describe any Regular Polygon upon a Given Right Line, Admitting the Division of a Given Arch of a Circle into any Number of Equal Parts.”, in E[dmund] Stone, transl., Euclid’s Elements of Geometry, the First Six, the Eleventh and Twelfth Books; […], London: […] Tho[mas] Payne, […], →OCLC, book IV, pages 199–200:

Bismuth is the most common of all native metallic substances. It is generally found either in cubes or octagons, or of a dendritical form, or else in thin laminæ investing the ores of other metals, particularly those of cobalt.

1808, William Nicholson, “Ores of Bismuth”, in A Dictionary of Practical and Theoretical Chemistry, […], London: […] Richard Phillips, […], →OCLC, column 2:

The font is an octagon, having at each angle a slender pillar with crockets and finials, and the sides are richly sculptured with angels and animals, the figures holding shields, with various devices; at each corner of the contracting part towards the pedestal, are cherubs heads with expanded wings; and the pedestal, which is an irregular octagon, is ornamented with four non-descript animals, scaled over their breasts; on a moulding round the bottom are several old characters, now illegible.

1810, [James Sargant Storer; John Grieg], “Worlingworth Church, Suffolk”, in Antiquarian and Topographical Cabinet, Containing a Series of Elegant Views of the Most Interesting Objects of Curiosity in Great Britain. […], volume VII, London: […] W. Clarke, […], →OCLC:

The building [the Winter Garden conservatory, Kew Gardens] was to be of five parts—a centre, two small octagons, and two wings connected by the octagons with the centre. The centre and the two octagons were finished, and some expenditure must have been laid out on the wings, as the ground was dug out and foundations in concrete laid for the pillars.

1863 June 1, [Charles William] Selwyn, “Supply—Civil Service Estimates. Supply Considered in Committee.”, in Hansard’s Parliamentary Debates, […] (House of Commons), volume CLXXI, London: Published by Cornelius Buck, at the office for “Hansard’s Parliamentary Debates,” […], →OCLC, columns 214–215:

China converted the hard octagons of the Turkoman rugs into circular scrolls or medallions, beautifying them meanwhile with floral character manifestly borrowed from the Persians and yet by no means Persian.

1922 October 28, Roy C. Bennett, “Rug Gift to National Press Club Typifies New China Industry”, in J[ohn] B[enjamin] Powell, editor, The Weekly Review, volume XXII, number 9, Shanghai: Millard Publishing Company, →OCLC, page 299, column 2:

(geometry, also attributively) A polygon with eight sides and eight angles.


arc

→ Irish: arc

→ Maltese: ark

→ Welsh: arc

Inherited from Middle English ark, from Old French arc, from Latin arcus (“a bow, arc, arch”), ultimately from Proto-Indo-European *h₂erkʷos (“bow, arrow”). Doublet of arch, arco, and arrow.

(geometry) A continuous part of the circumference of a circle (circular arc) or of another curve.


axis

Borrowed from Latin axis (“axle, axis”) in the 16th century.

A doorknob of whatever roundish shape is effectively a continuum of levers, with the axis of the latching mechanism—known as the spindle—being the fulcrum about which the turning takes place.

2012 March 18, Henry Petroski, “Opening Doors”, in American Scientist, volume 100, number 2, pages 112–3:

The Earth rotates once a day on its axis

(geometry) An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry).


rhombus

Learned borrowing from Latin rhombus, from Ancient Greek ῥόμβος (rhómbos, “rhombus, spinning top”). Doublet of rhomb and rhumb.

romb

(geometry) A parallelogram having all sides of equal length.

The rhombus diamond, as one of the suits seen in a deck of playing cards ( or ).


flag

en-noun

flag (countable and uncountable, plural flags)

From Middle English flag, flagge (“flag”), further etymology uncertain. Perhaps from or related to early Middle English flage (name for a baby's garment) and Old English flagg, flacg (“cataplasm, poultice, plaster”). Or, perhaps ultimately imitative, or otherwise drawn from Proto-Germanic *flaką (“something flat”), from Proto-Indo-European *pleh₂- (“flat, broad, plain”), referring to the shape.
Germanic cognates include Saterland Frisian Flaage (“flag”), West Frisian flagge (“flag”), Dutch vlag (“flag”), German Flagge (“flag”), Swedish flagga (“flag”), Danish flag (“flag, ship's flag”). Compare also Middle English flacken (“to flutter, palpitate”), Swedish dialectal flage (“to flutter in the wind”), Old Norse flögra (“to flap about”). Akin to Old High German flogarōn (“to flutter”), Old High German flogezen (“to flutter, flicker”), Middle English flakeren (“to move quickly to and fro”), Old English flacor (“fluttering, flying”). More at flack, flacker.

onomatopoeic

imitative

cog

A flag of P is a sequence (F₀, F₁, ..., Fₘ) of faces of P such that dim Fᵢ = i for each i and Fᵢ is a side of Fᵢ₊₁ for each i < m.[…]A regular polytope in X is a polytope P in X whose group of symmetries in <P> acts transitively on its flags.

1994, John Ratcliffe, Foundations of Hyperbolic Manifolds, page 230:

We call P (combinatorially) regular if its automorphism group Γ(P) is transitive on its flags.

2002, Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and Its Applications 92, page 31:

Roughly speaking, chiral polytopes have half as many possible automorphisms as have regular polytopes. More technically, the n-polytope P is chiral if it has two orbits of flags under its group Γ(P), with adjacent flags in different orbits.

2006, Peter McMullen, Egon Schulte, “Regular and Chiral Polytopes in Low Dimensions”, in Harold Scott Macdonald Coxeter, Chandler Davis, Erich W. Ellers, editors, The Coxeter Legacy: Reflections and Projections, page 91:

(geometry) A sequence of faces of a given polytope, one of each dimension up to that of the polytope (formally, though in practice not always explicitly, including the null face and the polytope itself), such that each face in the sequence is part of the next-higher dimension face.

lippu

geometry: sequence of faces of a polytope


witch

The noun is from Middle English wicche, from Old English wiċċe (“witch (female), sorceress”) and wiċċa (“witch (male), sorcerer, warlock”), deverbative from wiċċian (“to practice sorcery”), from Proto-Germanic *wikkōną (compare West Frisian wikje, wikke (“to foretell, warn”), German Low German wicken (“to soothsay”), Dutch wikken, wichelen (“to dowse, divine”)), from Proto-Indo-European *wik-néh₂-, derivation of *weyk- (“to consecrate; separate”); akin to Latin victima (“sacrificial victim”), Lithuanian viẽkas (“life-force”), Sanskrit विनक्ति (vinákti, “to set apart, separate out”). Possibly related to wicked; see that entry for more. The verb derives from the noun.

cog

(geometry) A certain curve of the third order, described by Maria Agnesi under the name versiera.


form

en-noun

form (countable and uncountable, plural forms)

→ Korean: 폼 (pom)

→ Norwegian Bokmål: form

From Middle English forme (“shape, figure, manner, bench, frame, seat, condition, agreement, etc.”), borrowed from Old French forme, from Latin fōrma (“shape, figure, image, outline, plan, mold, frame, case, etc., manner, sort, kind, etc.”).
In sense "division grouping school students" (now dated), derived from public school nomenclature later adopted by state schools. It is sometimes said to be from the sense of "bench", where students of certain ages would sit together, though this is disputed, or alternatively from the sense of "established method of expression or practice".

der

imitation is the sincerest form of flattery


pentagon

From Middle French pentagone, from Late Latin pentagōnum, from Ancient Greek πεντάγωνον (pentágōnon), noun use of the neuter of the adjective πεντάγωνος (pentágōnos, “five-angled”), from πέντε (pénte, “five”) + -γωνος (-gōnos, “angled”). Equivalent to penta- + -gon.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, […]

1884, A Square [pseudonym; Edwin A. Abbott], Flatland […] , London: Seeley & Co., Part I: This World, § 1.— Of the Nature of Flatland, page 3:

(geometry) A polygon with five sides and five angles.

pentagoon

a polygon with five sides and five angles


nonagon

(geometry) A polygon with nine sides and nine angles; an enneagon.


enneagon

(geometry) A polygon with nine sides; a nonagon.


decagon

(geometry) A polygon with ten sides and ten angles.


undecagon

LL-Q1860 (eng)-Flame, not lame-undecagon.wav

(geometry) A polygon with eleven sides and eleven angles.


dodecagon

LL-Q1860 (eng)-Flame, not lame-dodecagon.wav

(geometry) A polygon with twelve edges and twelve angles.


quindecagon

LL-Q1860 (eng)-Flame, not lame-quindecagon.wav

(geometry) A polygon with fifteen sides and fifteen angles.


honeycomb

en-noun

honeycomb (countable and uncountable, plural honeycombs)

Alhambra
Oxford English Dictionary
United States Army

The noun is derived from Middle English hony comb, from Old English huniġcamb, from huniġ (“honey”) (ultimately from Proto-Indo-European *kn̥h₂ónks (“honey”)) + camb (“comb”) (ultimately from Proto-Indo-European *ǵómbʰos (“peg; tooth; row of teeth”)). The English word is analysable as honey + comb. The Oxford English Dictionary posits that the arrangement of several plates of wax “hanging parallel to each other from the roof of the hive suggests a comb with its teeth”. The verb is derived from the noun.

kennosto

something resembling honeycomb in having numerous cells or small holes

hunaja

something resembling honeycomb in sweetness; something desirable or pleasant

(countable, by extension) Something resembling honeycomb (sense 1) in having numerous cells or small holes.

(countable, geometry) A space-filling packing of polytopes in three- or higher-dimensional space.


pair of compasses

en-noun

pair of compasses (plural pairs of compasses)

A tool for drawing accurate circles or circular arcs, or for measuring or transferring lengths, usually consisting of two arms joined with an adjustable hinge at one end; until the middle ages both arms always had metal points at their free ends (this version is now called a divider or pair of dividers), but in recent centuries for a device called a compass or pair of compasses, one arm typically holds a ruling pen, pencil, or some other implement for making marks.


ellipsis

ellipsis (countable and uncountable, plural ellipses)

Unadapted borrowing from Latin ellīpsis, from Ancient Greek ἔλλειψις (élleipsis, “omission”). Doublet of ellipse.


focus

en-noun

focus (countable and uncountable, plural foci or focuses or focusses)

foci (plural)
focuses (plural)
focusses (plural)

Borrowed from Latin focus (“hearth, fireplace”); see there for more. Doublet of fuel.
Kepler introduced the term into mathematics and the sciences in describing elliptical orbits of planets (quote from Nicholas Mee) :
"One of the interesting properties of an ellipse is that if there were a light bulb at one focus, then all the light that it emits would reflect off the ellipse and converge at the other focus. This is why Kepler originally used the name focus for these points."

bor+

(countable, geometry) A point of a conic at which rays reflected from a curve or surface converge.


sagitta

en-noun

sagitta (plural sagittas or (arrowworm) sagittae)

/səˈd͡ʒɪt.ə/

LL-Q1860 (eng)-Flame, not lame-sagitta.wav

Borrowing from Latin sagitta (“an arrow, shaft, bolt”).

(geometry) The distance from a point in a curve to the chord; also, the versed sine of an arc; so called from its resemblance to an arrow resting on the bow and string.


diamond

diamond (countable and uncountable, plural diamonds)

From Middle English dyamaunt, from Old French diamant, from Late Latin diamās, from Latin adamās, from Ancient Greek ἀδάμᾱς (adámās, “diamond”). Doublet of adamant. The printing sense is a calque of Dutch diamant, used by Dirck Voskens who first cut it around 1700; compare pearl, ruby (“size of type between pearl and nonpareil”).

der

An adder writhes out of the bush, I can see the diamonds on its back; it shrithes across the sandy soil, and bites the right foot of one of the knights.

2003, Kevin Crossley-Holland, “The Most Bitter Day”, in King of the Middle March (Arthur; 3), London: Orion Children's Books, →ISBN; 1st American edition, New York, N.Y.: Arthur A. Levine Books, Scholastic Inc., 2004 October, →ISBN, page 349:

(geometry) A rhombus, especially when oriented so that its longer axis is vertical.

(geometry) The polyiamond made up of two triangles.


envelope

PIE word
 *h₁én
From French enveloppe. The engineering sense is derived from flight envelope. The verb is from the noun.

(geometry) A mathematical curve, surface, or higher-dimensional object that is the tangent to a given family of lines, curves, surfaces, or higher-dimensional objects.

vaippa

geometry: object that is the tangent to a family of objects


gradian

LL-Q1860 (eng)-Flame, not lame-gradian.wav

Some information is available in Wikipedia at gradian § History and name.

(geometry, trigonometry) A unit of angle equal to 0.9 degree, so that there are 100 gradians in a right angle.


arch

From Middle English arch, arche, from Old French arche (“an arch”), a feminine form of arc, from Latin arcus (“a bow, arc, arch”). Doublet of arc and arco. Displaced native Old English bīeġels.

(archaic, geometry) An arc; a part of a curve.


diagonal

/daɪˈæɡənəl/

/dɑɪˈæɡ.ə.nəl/

From Middle French diagonal, from Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”), from διά (diá, “across”) + γωνία (gōnía, “angle”).

(geometry) Joining two nonadjacent vertices (of a polygon or polyhedron).

مَائِل

geometry: joining two nonadjacent vertices


diagonal

backslash

antonym(s) of “oblique punctuation mark”

/daɪˈæɡənəl/

/dɑɪˈæɡ.ə.nəl/

диагонал

something forming or resembling a diagonal line

(geometry) A line joining non-adjacent vertices of a polygon.

Anything forming or resembling such a line, particularly:

(geometry) A line or plane at an oblique angle to another.


hendecagon

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(geometry) A polygon with eleven edges and eleven angles.


chord

chords (plural)
cord (alternative dated)

Variant of cord, with spelling alteration due to Latin chorda (“cord”), ultimately from Ancient Greek χορδή (khordḗ, “string of gut, the string of a lyre”). No relation to French accord (“chord”) and its derivations.

The simplest method of calculating the radius of a curve in situ is to measure the versine; in railway practice this is done by extending a tape 66 ft. (1 ch.) long in a straight line or chord between two points on the periphery of a curve, and then measuring the maximum distance of the rail from the chord at the centre of the 66 ft. The radius in chains is found by dividing the versine in inches into 99. Thus if a versine measures 3 in., the radius will be 33 ch.

1941 September, “The Why and the Wherefore: Curves”, in Railway Magazine, page 430:

(geometry) A line segment between two points of a curve.


gnomon

Borrowed from French gnomon, or directly from its etymon Latin gnōmōn, or directly from its etymon Ancient Greek γνώμων (gnṓmōn, “discerner, interpreter; carpenter’s square; gnomon of a sundial; (geometry) gnomon”), from γιγνώσκω (gignṓskō, “to be aware of; to perceive; to know”), ultimately from Proto-Indo-European *ǵneh₃- (“to know”); the word is thus related to know.
The geometry sense (sense 4) is from the resemblance of the plane figure to a carpenter’s square. Similarly, a gnomon in mathematics (sense 5) is also shaped like a carpenter’s square when depicted pictorially if the figurate numbers are squares.

If a Parallelogram be divided into four leſſer ones, by two Lines interſecting each other; and one of theſe Parallelograms be retrench'd, or taken away; the other three will make a Gnomon, ordinarily call'd a Square.

1728, E[phraim] Chambers, “Gnomon”, in Cyclopædia: Or, An Universal Dictionary of Arts and Sciences; […] In Two Volumes, volumes I (A–H), London: […] James and John Knapton [et al.], →OCLC, page 164, column 2:

(geometry) A plane figure formed by removing a parallelogram from a corner of a larger parallelogram.


alternate

en-verb

alternate (third-person singular simple present alternates, present participle alternating, simple past and past participle alternated)

alternates (present singular third-person)
alternating (participle present)
alternated (participle past)
alternated (past)

Borrowed from Latin alternātus, the perfect passive participle of Latin alternō (“to take turns”) (see -ate (1,2 and 3)), from alternus (“one after another, by turns”), from alter (“other”) + -nus. Doublet of altern; see also alter.

This case suggests that the alternation of a polyhedron should be bounded by actual vertex figures and alternated faces. The case of the cube is in agreement with this notion, since the alternated square is nothing.

1932, Harold Scott Macdonald Coxeter, The densities of the regular polytopes, part 2, reprinted in 1995, F. Arthur Sherk, Peter Mcmullen, Anthony C. Thompson, Asia Ivić Weiss (editors), Kaleidoscopes: Selected Writings of H. S. M. Coxeter, page 54:

(transitive, geometry) To perform an alternation (removal of alternate vertices) on (a polytope or tessellation); to remove vertices (from a face or edge) as part of an alternation.


alternation

en-noun

alternation (countable and uncountable, plural alternations)

Learned borrowing from Latin alternatio; compare French alternation. By surface analysis, alternate + -ion.

1932, Harold Scott Macdonald Coxeter, The densities of the regular polytopes, part 2, reprinted in 1995, F. Arthur Sherk, Peter Mcmullen, Anthony C. Thompson, Asia Ivić Weiss (editors), Kaleidoscopes: Selected Writings of H. S. M. Coxeter, page 54,
This case suggests that the alternation of a polyhedron should be bounded by actual vertex figures and alternated faces. The case of the cube is in agreement with this notion, since the alternated square is nothing.

(geometry) A type of partial truncation of a polygon, polyhedron or tiling in which alternate vertices are removed.


height

height (countable and uncountable, plural heights)

heights (plural)
heighth (alternative obsolete)
heigth (alternative obsolete)
hight (alternative obsolete)
highth (alternative obsolete)

From Middle English heighte, heiȝþe, from Old English hēahþu, hēhþo, hīehþu (“height”), Proto-West Germanic *hauhiþu, from Proto-Germanic *hauhiþō (compare *hauhaz). Equivalent to high + -th (abstract nominal suffix).
Cognates
See also Saterland Frisian Höchte, Hööchte (“height”), West Frisian hichte (“height”), Dutch hoogte (“height”), Middle High German hœhede, hœhte (“height”), Old Norse and Old Norse hæð (“height”) (compare Swedish höjd, Norwegian høyde), Gothic 𐌷𐌰𐌿𐌷𐌹𐌸𐌰 (hauhiþa, “height”).

The area of a triangle is "a half base times height".

The distance from the base to the top of something.

(geometry) The minimum distance from a vertex of a triangle to (the extension of) the edge opposite, namely along a line perpendicular to the edge.


trace

From Middle English trace, traas, from Old French trace (“an outline, track, trace”), from the verb (see below).

der

(geometry) The intersection of a plane of projection, or an original plane, with a coordinate plane.


supplementary angles

A = 30° and A′ = 150°, so A and A′ are supplementary angles.

(geometry) A pair of angles that sum to 180 degrees.


complementary angles

Complementary in the sense of completing, i.e. they form a complete right angle.

A = 30° and A′ = 60°, so A and A′ are complementary angles.

(geometry) A pair of angles that sum to a right angle.


cyclic quadrilateral

en-noun

cyclic quadrilateral (plural cyclic quadrilaterals)

LL-Q1860 (eng)-Flame, not lame-cyclic quadrilateral.wav

(geometry) A quadrilateral whose vertices all intersect a single circle.


vertex

Late Middle English, borrowed from Latin vertex (“whirl, eddy; top, crown, peak, summit”). Doublet of vortex.

der

Mathworld article on vertices of polyhedra

Mathworld article on vertices of polygons

(geometry) An angular point of a polygon, polyhedron or higher order polytope.

The common point of the two rays that form an angle.

The point at which an axis meets a curve or surface.


edge

From Middle English egge, from Old English eċġ, from Proto-West Germanic *aggju, from Proto-Germanic *agjō, from Proto-Indo-European *h₂eḱ- (“sharp”).
See also Dutch egge, German Ecke, Swedish egg, Norwegian egg; also Welsh hogi (“to sharpen, hone”), Latin aciēs (“sharp”), acus (“needle”), Latvian ašs, ass (“sharp”), Ancient Greek ἀκίς (akís, “needle”), ἀκμή (akmḗ, “point”), and Persian آس (âs, “grinding stone”)).

(geometry) A one-dimensional face of a polytope. In particular, the joining line between two vertices of a polygon; the place where two faces of a polyhedron meet.


expansion

en-noun

expansion (countable and uncountable, plural expansions)

Borrowed from French expansion, from Latin expānsiō. By surface analysis, expand + -sion.

An act, process, or instance of expanding.

(geometry) Stretching of geometric objects with flat sides.


median

LL-Q1860 (eng)-I learned some phrases-median.wav

Borrowed from Middle French median, from Latin mediānus (“of or pertaining to the middle”, adjective), from medius (“middle”) (see medium), from Proto-Indo-European *médʰyos (“middle”). Doublet of mean and mizzen. Cognate with Old English midde, middel (“middle”). More at middle.

der

(geometry) A line segment joining the vertex of triangle to the midpoint of the opposing side.

median

geometry: line segment joining vertex and midpoint of opposing side


octahedron

en-noun

octahedron (plural octahedra or octahedrons)

octahedra (plural)
octahedrons (plural)
octohedron (alternative)

From Ancient Greek ὀκτάεδρον (oktáedron). By surface analysis, octa- + -hedron.

(geometry) a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.


inverse

Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“in, on”) + vertere (“to turn”).

A circle inversion maps a given generalized circle to its inverse generalized circle.

(geometry) That has the property of being an inverse (the result of a circle inversion of a given point or geometrical figure); that is constructed by circle inversion.


inverse

противоположност

opposite of a given due to contrary effects or nature

The inverse P‘ of a point P is the point on a ray from the center O through P such that OP × OP‘ = r² or the set of all such points.

The result of an inversion, particularly:

(geometry) The result of a circle inversion; the set of all such points; the curve described by such a set.


Platonic solid

Platonic solids (plural)
platonic solid (alternative)

From Platonic + solid, in reference to the Greek philosopher Plato, who in his dialogue Timaeus theorised about a correspondence between these solids and the classical physical elements.

As the names suggest, the groups and their existence are connected to the five Platonic solids. They are in fact the rotation groups of the Platonic solids.

1961, J. S. Griffith, The Theory of Transition-Metal Ions, page 41:

The boat which the gods tell Utnapishtim to build is no ordinary boat but a perfect cube with seven levels; the ark resembles more a Platonic solid from the Timaeus than a seaworthy craft.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 202:

The erroneous number of planets, six, gave him^([Johannes Kepler]) the clue for his model of five Platonic solids (the five regular convex polyhedra) on which he erected the universe.

1993, Aharon Kantorovich, Scientific Discovery: Logic and Tinkering, page 160:

In the 13th and final book, he^([Euclid]) shows how to construct the five Platonic solids, and proves that they are the only regular polyhedra (bodies whose faces are congruent, regular polygons) that exist.

2015, Alexander A. Stepanov, Daniel E. Rose, From Mathematics to Generic Programming, page 44:

(geometry) Any of five convex polyhedra with congruent regular polygonal faces, which have a high degree of symmetry and have been studied since antiquity.

Classical element
Platonic solid
Timaeus (dialogue)


Kepler solid

(geometry) Any of several nonconvex regular polyhedra with regular pentagrammatic faces or vertex figures and which can be obtained by stellation of the dodecahedron or icosahedron.

Johannes Kepler
Kepler–Poinsot polyhedron
great stellated dodecahedron


trigon

trigon (countable and uncountable, plural trigons)

From Ancient Greek τρίγωνον (trígōnon, “triangle”), neuter substantive of τρίγωνος (trígōnos, “three-sided”), from τρεῖς (treîs, “three”) + γωνία (gōnía, “bend, angle”). Equivalent to tri- + -gon. Doublet of trigone and trigonon.


parameter

[pəˈɹæm.ə.ɾɚ]

/pəˈɾamˌiːʈə(ɾ)/

From French paramètre, from New Latin parametrum (“parameter”), from Ancient Greek παρα- (para-, “beside”) + μέτρον (métron, “measure”).

The parameter of the principal axis of a conic section is called the latus rectum.

(geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.


-gon

From Ancient Greek γωνία (gōnía, “corner, angle”), from Proto-Indo-European *ǵónu (“knee”).

bor

A pentagon has five sides.

a 17-gon

(geometry) Forms the names of plane figures containing a given number of angles, and thus bounded by that number of line segments (polygons). If the number is large enough, it can take the hyphenated suffix directly.


-hedron

LL-Q1860 (eng)-Flame, not lame--hedron.wav

From Ancient Greek ἕδρα (hédra, “face of a geometrical solid”).

der

(geometry) Forms the names of solid figures bounded by a certain number of planes (polyhedra).


complement

en-noun

complement (countable and uncountable, plural complements)

From Middle English complement, from Latin complēmentum (“that which fills up or completes”), from compleō (“I fill up, I complete”) (English complete). Doublet of compliment. The verb is from the noun.

der

(astronomy, geometry) An angle which, together with a given angle, makes a right angle.


cap

Inherited from Middle English cappe, from Old English cæppe, from Proto-West Germanic *kappā (“covering, hood, mantle”), from Late Latin cappa, itself from Latin caput. Ultimately from Proto-Indo-European *káput- and Proto-Indo-European *kap- (“head”). Doublet of cape, chape, and cope.

nalli

small amount of explosive used as detonator

(geometry) A portion of a spherical or other convex surface.


term

From Middle English terme, borrowed from Old French terme, from Latin terminus (“a bound, boundary, limit, end; in Medieval Latin, also a time, period, word, covenant, etc.”), ultimately from Proto-Indo-European *térmn̥ (“stump, end, boundary”).
Doublet of terminus and termon. Old English had termen, from the same source.

términu

one of the addends in a sum or in another mathematical operation

A line is the term of a superficies, and a superficies is the term of a solid.

(geometry, archaic) A point, line, or superficies that limits.


congruence

en-noun

congruence (countable and uncountable, plural congruences)

/ˈkɒŋ.ɡɹʊ.əns/

/ˈkɔŋ.ɡɹʉ.əns/

From Middle English congruence, from Latin congruentia (“agreement”), from congruēns, present active participle of congruō (“meet together, agree”).

համաձայնություն

the quality of agreeing or corresponding

(mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.

全等

geometry, quality of being roughly the same size and shape


simplex

simplex (plural simplexes or (algebraic topology, geometry, linguistics) simplices or simplicia)

simplexes (plural)
simplices (plural)
simplicia (plural)

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplex.wav

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplices.wav

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-simplicia.wav

Henri Poincaré
MacTutor History of Mathematics Archive
Pieter Hendrik Schoute

The adjective is a learned borrowing from Latin simplex (“plain, simple; single”). The first part, sim-, comes from Proto-Indo-European *sem-, *sm̥- (“one; together”). The second part, -plex, may be from *pleḱ- (“to weave”).
The noun is derived from the adjective. The plural forms simplices and simplicia are learned borrowings from Latin simplicēs (masculine or feminine) and simplicia (neuter), respectively plural forms of simplex.
Noun sense 1 (“generalization of a triangle or tetrahedron to an arbitrary dimension”) was apparently coined by the Dutch mathematician Pieter Hendrik Schoute (1846–1913) as a short version of Simplicissimum in Mehrdimensionale Geometrie (in German, 1902). (In his pioneering works on algebraic topology, the French mathematician Henri Poincaré (1854–1912) had previously introduced the concept, but not the actual term simplex.)

lbor

affinely independent
affinely independent

(algebraic topology, geometry) A generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.