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


pyramid

pyramid (indefinite nominative singular)
pyramids (genitive indefinite singular)
pyramiden (definite nominative singular)
pyramidens (definite genitive singular)
pyramider (indefinite nominative plural)
pyramiders (genitive indefinite plural)
pyramiderna (definite nominative plural)
pyramidernas (definite genitive plural)


với

head

众, 喟, 某, 貝, 買, 𠇍

vi-prep

众, 喟, 某, 貝, 買, 𠇍

众 (CJK)
喟 (CJK)
某 (CJK)
貝 (CJK)
買 (CJK)
𠇍 (CJK)
vuối (alternative)
vs (alternative)
dí (alternative)

Cognate with Muong Bi pỡi.
Probably related as etymology 1, as prepositions in Vietnamese are most often originally verbals.
The form vuối used to enjoy widespread usage in both Northern and Southern dialects, but is now completely obsolete. This form might be the diphthongized equivalent of vói (“to stretch out, to reach out”) mentioned above.

LL-Q9199 (vie)-Jessica Nguyen (Pamputt)-với.wav

góc ABC kề với góc CBD

đường thẳng d song song/vuông góc với đường thẳng e/mặt phẳng p

line d is parallel/perpendicular to line e/plane p

(geometry, after kề (“adjacent”), bù (“supplementary”), song song (“parallel”), vuông góc (“perpendicular”), etc.) to


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


steradian

steradian (nominative singular)
steradiany (nominative plural)
steradiana (genitive singular)
steradianów (genitive plural)
steradianowi (dative singular)
steradianom (dative plural)
steradian (accusative singular)
steradiany (accusative plural)
steradianem (instrumental singular)
steradianami (instrumental plural)
steradianie (locative singular)
steradianach (locative plural)
steradianie (singular vocative)
steradiany (plural vocative)

(geometry) steradian (derived unit of solid angle; the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere that has area r²)


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”)


radius

head

radius c (singular definite radien or radiusen, plural indefinite radier or radiuser)

radien (definite singular)
radiusen (definite singular)
radier (indefinite plural)
radiuser (indefinite plural)


radius

fo-noun

radius m (genitive singular radius, plural radiusar)

radius (genitive singular)
radiusar (plural)
radius (indefinite nominative singular)
radiusin (definite nominative singular)
radiusar (indefinite nominative plural)
radiusarnir (definite nominative plural)
radius (accusative indefinite singular)
radiusin (accusative definite singular)
radiusar (accusative indefinite plural)
radiusarnar (accusative definite plural)
radiusi (dative indefinite singular)
radiusinum (dative definite singular)
radiusum (dative indefinite plural)
radiusunum (dative definite plural)
radius (genitive indefinite singular)
radiussins (definite genitive singular)
radiusa (genitive indefinite plural)
radiusanna (definite genitive plural)


radius

head

radius m (definite singular radien or radiusen, indefinite plural radier, definite plural radiene)

radien (definite singular)
radiusen (definite singular)
radier (indefinite plural)
radiene (definite plural)


radius

radius m (definite singular radiusen, indefinite plural radiusar, definite plural radiusane)

radiusen (definite singular)
radiusar (indefinite plural)
radiusane (definite plural)


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


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.


arc

Inherited from Latin arcus, from Proto-Indo-European *h₂erkʷo-.


arc

Inherited from Old French arc, from Latin arcus (“bow, arch”), from Proto-Indo-European *h₂erkʷo-.

(geometry) arc, circular arc, circle segment


arc

head

arc m (genitive singular airc, nominative plural airc)

airc (genitive singular)
airc (nominative plural)

Borrowed from Anglo-Norman arc, from Latin arcus (“a bow, arc, arch”).


arc

arce (plural)
arc (accusative indefinite nominative singular)
arcul (accusative definite nominative singular)
arce (accusative indefinite nominative plural)
arcele (accusative definite nominative plural)
arc (indefinite singular)
arcului (definite singular)
arce (indefinite plural)
arcelor (definite plural)
arcule (singular vocative)
arcelor (plural vocative)


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 22, 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.


plan

→ Central Franconian: Plan

Hunsrik: Plaan

→ German: Plan

→ Norwegian Bokmål: plan

→ Luxembourgish: Plang

→ Ottoman Turkish: پلان
Turkish: plan

→ Persian: پلان (pelân)

→ Polish: plan
→ Kashubian: plan

From earlier plant, derived from the verb planter, or from Latin planus. Doublet of plant or plain, depending on which etymology is right.


plan

planuri (plural)
plan (accusative indefinite nominative singular)
planul (accusative definite nominative singular)
planuri (accusative indefinite nominative plural)
planurile (accusative definite nominative plural)
plan (indefinite singular)
planului (definite singular)
planuri (indefinite plural)
planurilor (definite plural)
planule (singular vocative)
planurilor (plural vocative)

Borrowed from French plan, from Latin planus.


proper

en-adj

proper (comparative more proper, superlative most proper)

more proper (comparative)
most proper (superlative)
propa (alternative Geordie)
propre (alternative obsolete)

From Middle English propre, from Anglo-Norman proper, propre, Old French propre (French: propre), from Latin proprius.

luonnonvärinen

heraldry: having its natural or usual coloration

(algebraic geometry, of a morphism of schemes) Separated, of finite type, and universally closed.

(algebraic geometry, of a variety over a field k) Such that unique morphism from the variety to k is proper (as above).


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


pentagon

pentagon m (definite singular pentagonen, indefinite plural pentagoner, definite plural pentagonene)

pentagonen (definite singular)
pentagoner (indefinite plural)
pentagonene (definite plural)


pentagon

pentagon m (definite singular pentagonen, indefinite plural pentagonar, definite plural pentagonane)

pentagonen (definite singular)
pentagonar (indefinite plural)
pentagonane (definite plural)


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.


local

en-adj

local (comparative more local, superlative most local)

more local (comparative)
most local (superlative)

From Middle English local, from Late Latin locālis (“belonging to a place”), possibly also via Old French local; ultimately from Latin locus (“a place”).
The ring-theoretic senses derive from Krull, who first referred to Noetherian commutative rings with a unique maximal ideal as "Stellenring" (Stellen (“place”) + ring) in 1938. The term was inspired by algebraic geometry, where local rings encode information about the behavior of curves (surfaces, etc.) at points; hence, describe "local" behavior.

der

Flatness is a local property.

(mathematics, not comparable, of a condition or property) Detectable from the behavior of substructures understood to be "near points;" in particular:

(algebra, algebraic geometry, of a property P of a ring R (or an R-module M)) Such that the following conditions are equivalent: (1) P holds for R (M); (2) P holds for the localization R_p (M_p) for all prime ideals p of R; (3) P holds for the localization R_m (M_m) for all maximal ideals m of R.


ellipsis

en-noun

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/

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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

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


él

élek (plural)
él (nominative singular)
élek (nominative plural)
élt (accusative singular)
éleket (accusative plural)
élnek (dative singular)
éleknek (dative plural)
éllel (instrumental singular)
élekkel (instrumental plural)
élért (causal-final singular)
élekért (causal-final plural)
éllé (singular translative)
élekké (plural translative)
élig (singular terminative)
élekig (plural terminative)
élként (essive-formal singular)
élekként (essive-formal plural)
élben (inessive singular)
élekben (inessive plural)
élen (singular superessive)
éleken (plural superessive)
élnél (adessive singular)
éleknél (adessive plural)
élbe (illative singular)
élekbe (illative plural)
élre (singular sublative)
élekre (plural sublative)
élhez (allative singular)
élekhez (allative plural)
élből (elative singular)
élekből (elative plural)
élről (delative singular)
élekről (delative plural)
éltől (ablative singular)
élektől (ablative plural)
élé (singular)
éleké (plural)
éléi (singular)
élekéi (plural)
élem (first-person possessed-single possessive singular)
éleim (first-person possessed-many possessive singular)
éled (possessed-single possessive second-person singular)
éleid (possessed-many possessive second-person singular)
éle (possessed-single possessive singular third-person)
élei (possessed-many possessive singular third-person)
élünk (first-person plural possessed-single possessive)
éleink (first-person plural possessed-many possessive)
életek (plural possessed-single possessive second-person)
éleitek (plural possessed-many possessive second-person)
élük (plural possessed-single possessive third-person)
éleik (plural possessed-many possessive third-person)

Probably from Proto-Ugric *elɜ (“edge”). Compare with Northern Mansi э̄лми (è̄lmi, “edge”).

(geometry) side (a bounding straight edge of a two-dimensional shape)


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.


diagonal

diagonal (nominative singular)
diagonale (nominative plural)
diagonalu (genitive singular)
diagonali (genitive plural)
diagonalów (genitive plural)
diagonalowi (dative singular)
diagonalom (dative plural)
diagonal (accusative singular)
diagonale (accusative plural)
diagonalem (instrumental singular)
diagonalami (instrumental plural)
diagonalu (locative singular)
diagonalach (locative plural)
diagonalu (singular vocative)
diagonale (plural vocative)
djagonal (alternative)


diagonal

(geometry) diagonal (joining two nonadjacent vertices)


diagonal

(geometry) diagonal (diagonal line or plane)


corda

Inherited from Latin chorda, from Ancient Greek χορδή (khordḗ, “rope, cord”).

a casa d'un penjat no hi anomenis cordes

tant s'estira la corda, que a la fi es trenca


corda

From Latin chorda (“cord”), from Ancient Greek χορδή (khordḗ, “string of gut, the string of a lyre”).


hendecagon

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


bok

boczny (adjective)
bok (nominative singular)
boki (nominative plural)
boku (genitive singular)
boków (genitive plural)
bokowi (dative singular)
bokom (dative plural)
bok (accusative singular)
boki (accusative plural)
bokiem (instrumental singular)
bokami (instrumental plural)
boku (locative singular)
bokach (locative plural)
boku (singular vocative)
boki (plural vocative)

(geometry) side (segment connecting two vertices of a polygon)


kon

kon (indefinite nominative singular)
kons (genitive indefinite singular)
konen (definite nominative singular)
konens (definite genitive singular)
koner (indefinite nominative plural)
koners (genitive indefinite plural)
konerna (definite nominative plural)
konernas (definite genitive plural)

Ultimately from Ancient Greek κῶνος (kônos).


dik

From Ottoman Turkish دیك (dik), from Proto-Turkic *tik-. Cognate with Old Turkic [script needed] (tik), ultimately from Middle Chinese 直 (drik).

(geometry) perpendicular; having a right angle


faccia

it-noun

faccia f (plural facce, diminutive faccétta or faccìna or faccìno m, augmentative faccióna or (more common) faccióne m, pejorative facciàccia, augmentative-endearing facciòtta)

facce (plural)
faccétta (diminutive)
faccìna (diminutive)
faccìno (diminutive masculine)
faccióna (augmentative)
faccióne (augmentative common masculine)
facciàccia (pejorative)

→ Catalan: fatxa

→ Greek: φάτσα (fátsa)

→ Occitan: facha (Niçard)

→ Sardinian: fàcia, fatza

From Late Latin facia, from Latin faciēs (“face”).


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.

der

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.


angular

ca-adj

angular m or f (masculine and feminine plural angulars)


angular

(geometry) angular (of or relating to angles)


angular

Borrowed from Latin angulāris (“angular”), from angulus (“corner; angle”), from Proto-Indo-European *h₂engulos.


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.


ympyrä

ympyrä (nominative singular)
ympyrät (nominative plural)
ympyrä (accusative nominative singular)
ympyrät (accusative nominative plural)
ympyrän (accusative genitive singular)
ympyrät (accusative genitive plural)
ympyrän (genitive singular)
ympyröiden (genitive plural)
ympyröitten (genitive plural)
ympyräin (genitive plural rare)
ympyrää (partitive singular)
ympyröitä (partitive plural)
ympyrässä (inessive singular)
ympyröissä (inessive plural)
ympyrästä (elative singular)
ympyröistä (elative plural)
ympyrään (illative singular)
ympyröihin (illative plural)
ympyrällä (adessive singular)
ympyröillä (adessive plural)
ympyrältä (ablative singular)
ympyröiltä (ablative plural)
ympyrälle (allative singular)
ympyröille (allative plural)
ympyränä (essive singular)
ympyröinä (essive plural)
ympyräksi (singular translative)
ympyröiksi (plural translative)
ympyrättä (abessive singular)
ympyröittä (abessive plural)
ympyröin (instructive plural)
See the possessive forms below. (comitative)
ympyräni (nominative singular)
ympyräni (nominative plural)
ympyräni (accusative nominative singular)
ympyräni (accusative nominative plural)
ympyräni (accusative genitive singular)
ympyräni (accusative genitive plural)
ympyräni (genitive singular)
ympyröideni (genitive plural)
ympyröitteni (genitive plural)
ympyräini (genitive plural rare)
ympyrääni (partitive singular)
ympyröitäni (partitive plural)
ympyrässäni (inessive singular)
ympyröissäni (inessive plural)
ympyrästäni (elative singular)
ympyröistäni (elative plural)
ympyrääni (illative singular)
ympyröihini (illative plural)
ympyrälläni (adessive singular)
ympyröilläni (adessive plural)
ympyrältäni (ablative singular)
ympyröiltäni (ablative plural)
ympyrälleni (allative singular)
ympyröilleni (allative plural)
ympyränäni (essive singular)
ympyröinäni (essive plural)
ympyräkseni (singular translative)
ympyröikseni (plural translative)
ympyrättäni (abessive singular)
ympyröittäni (abessive plural)
ympyröineni (comitative plural)
ympyräsi (nominative singular)
ympyräsi (nominative plural)
ympyräsi (accusative nominative singular)
ympyräsi (accusative nominative plural)
ympyräsi (accusative genitive singular)
ympyräsi (accusative genitive plural)
ympyräsi (genitive singular)
ympyröidesi (genitive plural)
ympyröittesi (genitive plural)
ympyräisi (genitive plural rare)
ympyrääsi (partitive singular)
ympyröitäsi (partitive plural)
ympyrässäsi (inessive singular)
ympyröissäsi (inessive plural)
ympyrästäsi (elative singular)
ympyröistäsi (elative plural)
ympyrääsi (illative singular)
ympyröihisi (illative plural)
ympyrälläsi (adessive singular)
ympyröilläsi (adessive plural)
ympyrältäsi (ablative singular)
ympyröiltäsi (ablative plural)
ympyrällesi (allative singular)
ympyröillesi (allative plural)
ympyränäsi (essive singular)
ympyröinäsi (essive plural)
ympyräksesi (singular translative)
ympyröiksesi (plural translative)
ympyrättäsi (abessive singular)
ympyröittäsi (abessive plural)
ympyröinesi (comitative plural)
ympyrämme (nominative singular)
ympyrämme (nominative plural)
ympyrämme (accusative nominative singular)
ympyrämme (accusative nominative plural)
ympyrämme (accusative genitive singular)
ympyrämme (accusative genitive plural)
ympyrämme (genitive singular)
ympyröidemme (genitive plural)
ympyröittemme (genitive plural)
ympyräimme (genitive plural rare)
ympyräämme (partitive singular)
ympyröitämme (partitive plural)
ympyrässämme (inessive singular)
ympyröissämme (inessive plural)
ympyrästämme (elative singular)
ympyröistämme (elative plural)
ympyräämme (illative singular)
ympyröihimme (illative plural)
ympyrällämme (adessive singular)
ympyröillämme (adessive plural)
ympyrältämme (ablative singular)
ympyröiltämme (ablative plural)
ympyrällemme (allative singular)
ympyröillemme (allative plural)
ympyränämme (essive singular)
ympyröinämme (essive plural)
ympyräksemme (singular translative)
ympyröiksemme (plural translative)
ympyrättämme (abessive singular)
ympyröittämme (abessive plural)
ympyröinemme (comitative plural)
ympyränne (nominative singular)
ympyränne (nominative plural)
ympyränne (accusative nominative singular)
ympyränne (accusative nominative plural)
ympyränne (accusative genitive singular)
ympyränne (accusative genitive plural)
ympyränne (genitive singular)
ympyröidenne (genitive plural)
ympyröittenne (genitive plural)
ympyräinne (genitive plural rare)
ympyräänne (partitive singular)
ympyröitänne (partitive plural)
ympyrässänne (inessive singular)
ympyröissänne (inessive plural)
ympyrästänne (elative singular)
ympyröistänne (elative plural)
ympyräänne (illative singular)
ympyröihinne (illative plural)
ympyrällänne (adessive singular)
ympyröillänne (adessive plural)
ympyrältänne (ablative singular)
ympyröiltänne (ablative plural)
ympyrällenne (allative singular)
ympyröillenne (allative plural)
ympyränänne (essive singular)
ympyröinänne (essive plural)
ympyräksenne (singular translative)
ympyröiksenne (plural translative)
ympyrättänne (abessive singular)
ympyröittänne (abessive plural)
ympyröinenne (comitative plural)
ympyränsä (nominative singular)
ympyränsä (nominative plural)
ympyränsä (accusative nominative singular)
ympyränsä (accusative nominative plural)
ympyränsä (accusative genitive singular)
ympyränsä (accusative genitive plural)
ympyränsä (genitive singular)
ympyröidensä (genitive plural)
ympyröittensä (genitive plural)
ympyräinsä (genitive plural rare)
ympyräänsä (partitive singular)
ympyröitään (partitive plural)
ympyröitänsä (partitive plural)
ympyrässään (inessive singular)
ympyrässänsä (inessive singular)
ympyröissään (inessive plural)
ympyröissänsä (inessive plural)
ympyrästään (elative singular)
ympyrästänsä (elative singular)
ympyröistään (elative plural)
ympyröistänsä (elative plural)
ympyräänsä (illative singular)
ympyröihinsä (illative plural)
ympyrällään (adessive singular)
ympyrällänsä (adessive singular)
ympyröillään (adessive plural)
ympyröillänsä (adessive plural)
ympyrältään (ablative singular)
ympyrältänsä (ablative singular)
ympyröiltään (ablative plural)
ympyröiltänsä (ablative plural)
ympyrälleen (allative singular)
ympyrällensä (allative singular)
ympyröilleen (allative plural)
ympyröillensä (allative plural)
ympyränään (essive singular)
ympyränänsä (essive singular)
ympyröinään (essive plural)
ympyröinänsä (essive plural)
ympyräkseen (singular translative)
ympyräksensä (singular translative)
ympyröikseen (plural translative)
ympyröiksensä (plural translative)
ympyrättään (abessive singular)
ympyrättänsä (abessive singular)
ympyröittään (abessive plural)
ympyröittänsä (abessive plural)
ympyröineen (comitative plural)
ympyröinensä (comitative plural)

Coined by Finnish physician and translator Wolmar Schildt in 1835 as a shortening (perhaps back-formation) of the dialectal terms ympyriäinen, ymmyrkäinen (“round”), ultimately from ympäri. The -ä- in ympäri- has turned into an -y- in these derivatives and thus in ympyrä as well, probably by influence from the preceding sounds (labial ymm-, ymp-). Arguably analyzable as ymp- + -yrä.


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


median

médian (canonical)
median-median (plural)

From Dutch mediaan, from Latin medianus (“of or pertaining to the middle”, adjective), from medius (“middle”) (see medium), from Proto-Indo-European *médʰyos (“middle”). Doublet of madya.

(geometry) a line segment joining the vertex of triangle to the midpoint of the 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.


punto

From English point, French point, German Punkt, Italian punto, Russian пункт (punkt), Spanish punto, all ultimately from Latin punctum.

(geometry, astronomy, typography, grammar, music, games) point; dot; position; period; small hole (as made by a needle or awl)

puntizar

to dot, prick, mark (something) with a point; to punctuate


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.


-gon

ca-noun

-gon m (noun-forming suffix, plural -gons)

Borrowed from Ancient Greek γωνία (gōnía).


-gon

Ultimately from Ancient Greek γωνία (gōnía).


-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).


kulma

kulma (nominative singular)
kulmat (nominative plural)
kulma (accusative nominative singular)
kulmat (accusative nominative plural)
kulman (accusative genitive singular)
kulmat (accusative genitive plural)
kulman (genitive singular)
kulmien (genitive plural)
kulmain (genitive plural rare)
kulmaa (partitive singular)
kulmia (partitive plural)
kulmassa (inessive singular)
kulmissa (inessive plural)
kulmasta (elative singular)
kulmista (elative plural)
kulmaan (illative singular)
kulmiin (illative plural)
kulmalla (adessive singular)
kulmilla (adessive plural)
kulmalta (ablative singular)
kulmilta (ablative plural)
kulmalle (allative singular)
kulmille (allative plural)
kulmana (essive singular)
kulmina (essive plural)
kulmaksi (singular translative)
kulmiksi (plural translative)
kulmatta (abessive singular)
kulmitta (abessive plural)
kulmin (instructive plural)
See the possessive forms below. (comitative)
kulmani (nominative singular)
kulmani (nominative plural)
kulmani (accusative nominative singular)
kulmani (accusative nominative plural)
kulmani (accusative genitive singular)
kulmani (accusative genitive plural)
kulmani (genitive singular)
kulmieni (genitive plural)
kulmaini (genitive plural rare)
kulmaani (partitive singular)
kulmiani (partitive plural)
kulmassani (inessive singular)
kulmissani (inessive plural)
kulmastani (elative singular)
kulmistani (elative plural)
kulmaani (illative singular)
kulmiini (illative plural)
kulmallani (adessive singular)
kulmillani (adessive plural)
kulmaltani (ablative singular)
kulmiltani (ablative plural)
kulmalleni (allative singular)
kulmilleni (allative plural)
kulmanani (essive singular)
kulminani (essive plural)
kulmakseni (singular translative)
kulmikseni (plural translative)
kulmattani (abessive singular)
kulmittani (abessive plural)
kulmineni (comitative plural)
kulmasi (nominative singular)
kulmasi (nominative plural)
kulmasi (accusative nominative singular)
kulmasi (accusative nominative plural)
kulmasi (accusative genitive singular)
kulmasi (accusative genitive plural)
kulmasi (genitive singular)
kulmiesi (genitive plural)
kulmaisi (genitive plural rare)
kulmaasi (partitive singular)
kulmiasi (partitive plural)
kulmassasi (inessive singular)
kulmissasi (inessive plural)
kulmastasi (elative singular)
kulmistasi (elative plural)
kulmaasi (illative singular)
kulmiisi (illative plural)
kulmallasi (adessive singular)
kulmillasi (adessive plural)
kulmaltasi (ablative singular)
kulmiltasi (ablative plural)
kulmallesi (allative singular)
kulmillesi (allative plural)
kulmanasi (essive singular)
kulminasi (essive plural)
kulmaksesi (singular translative)
kulmiksesi (plural translative)
kulmattasi (abessive singular)
kulmittasi (abessive plural)
kulminesi (comitative plural)
kulmamme (nominative singular)
kulmamme (nominative plural)
kulmamme (accusative nominative singular)
kulmamme (accusative nominative plural)
kulmamme (accusative genitive singular)
kulmamme (accusative genitive plural)
kulmamme (genitive singular)
kulmiemme (genitive plural)
kulmaimme (genitive plural rare)
kulmaamme (partitive singular)
kulmiamme (partitive plural)
kulmassamme (inessive singular)
kulmissamme (inessive plural)
kulmastamme (elative singular)
kulmistamme (elative plural)
kulmaamme (illative singular)
kulmiimme (illative plural)
kulmallamme (adessive singular)
kulmillamme (adessive plural)
kulmaltamme (ablative singular)
kulmiltamme (ablative plural)
kulmallemme (allative singular)
kulmillemme (allative plural)
kulmanamme (essive singular)
kulminamme (essive plural)
kulmaksemme (singular translative)
kulmiksemme (plural translative)
kulmattamme (abessive singular)
kulmittamme (abessive plural)
kulminemme (comitative plural)
kulmanne (nominative singular)
kulmanne (nominative plural)
kulmanne (accusative nominative singular)
kulmanne (accusative nominative plural)
kulmanne (accusative genitive singular)
kulmanne (accusative genitive plural)
kulmanne (genitive singular)
kulmienne (genitive plural)
kulmainne (genitive plural rare)
kulmaanne (partitive singular)
kulmianne (partitive plural)
kulmassanne (inessive singular)
kulmissanne (inessive plural)
kulmastanne (elative singular)
kulmistanne (elative plural)
kulmaanne (illative singular)
kulmiinne (illative plural)
kulmallanne (adessive singular)
kulmillanne (adessive plural)
kulmaltanne (ablative singular)
kulmiltanne (ablative plural)
kulmallenne (allative singular)
kulmillenne (allative plural)
kulmananne (essive singular)
kulminanne (essive plural)
kulmaksenne (singular translative)
kulmiksenne (plural translative)
kulmattanne (abessive singular)
kulmittanne (abessive plural)
kulminenne (comitative plural)
kulmansa (nominative singular)
kulmansa (nominative plural)
kulmansa (accusative nominative singular)
kulmansa (accusative nominative plural)
kulmansa (accusative genitive singular)
kulmansa (accusative genitive plural)
kulmansa (genitive singular)
kulmiensa (genitive plural)
kulmainsa (genitive plural rare)
kulmaansa (partitive singular)
kulmiaan (partitive plural)
kulmiansa (partitive plural)
kulmassaan (inessive singular)
kulmassansa (inessive singular)
kulmissaan (inessive plural)
kulmissansa (inessive plural)
kulmastaan (elative singular)
kulmastansa (elative singular)
kulmistaan (elative plural)
kulmistansa (elative plural)
kulmaansa (illative singular)
kulmiinsa (illative plural)
kulmallaan (adessive singular)
kulmallansa (adessive singular)
kulmillaan (adessive plural)
kulmillansa (adessive plural)
kulmaltaan (ablative singular)
kulmaltansa (ablative singular)
kulmiltaan (ablative plural)
kulmiltansa (ablative plural)
kulmalleen (allative singular)
kulmallensa (allative singular)
kulmilleen (allative plural)
kulmillensa (allative plural)
kulmanaan (essive singular)
kulmanansa (essive singular)
kulminaan (essive plural)
kulminansa (essive plural)
kulmakseen (singular translative)
kulmaksensa (singular translative)
kulmikseen (plural translative)
kulmiksensa (plural translative)
kulmattaan (abessive singular)
kulmattansa (abessive singular)
kulmittaan (abessive plural)
kulmittansa (abessive plural)
kulmineen (comitative plural)
kulminensa (comitative plural)

From Proto-Finnic *kulma, from Proto-Finno-Ugric *kuľma (“corner of the eye”), cognate to Karelian kulma, Estonian kulm and Eastern Khanty кулӛм (kuljəm, “temple (of the skull)”).

cog

Eulerin kulmat

(geometry) angle (geometrical figure; measure)


bue

head

bue c (singular definite buen, plural indefinite buer)

buen (definite singular)
buer (indefinite plural)
bue (indefinite nominative singular)
buen (definite nominative singular)
buer (indefinite nominative plural)
buerne (definite nominative plural)
bues (genitive indefinite singular)
buens (definite genitive singular)
buers (genitive indefinite plural)
buernes (definite genitive plural)

From Old Norse bogi, from Proto-Germanic *bugô, cognate with Swedish båge, English bow, German Bogen.


bue

bue m (definite singular buen, indefinite plural buer, definite plural buene)

buen (definite singular)
buer (indefinite plural)
buene (definite plural)
boge (alternative)

From Danish bue, from Old Norse bogi, from Proto-Germanic *bugô.

no:bue (arkitektur)
no:bue (geometri)
no:bue (våpen)


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


arco

Inherited from Old Galician-Portuguese arco, from Latin arcus, from Proto-Italic *arkuos.


arco

From Latin arcus, from Proto-Indo-European *h₂erkʷo- (“bow, arrow”).


arco

From Old Galician-Portuguese arco, arquo (“arch, bow”), from Latin arcus (“bow”), from Proto-Indo-European *h₂erkʷo- (“bow, arrow”).


arco

Inherited from Latin arcus (whence English archery), from Proto-Indo-European *h₂erkʷo- (“bow, arrow”). In some senses inherited, in others borrowed directly from Latin. Cognate with English arrow, arc, and arch.


segundo

segundos (plural)
2º (alternative)
2ª (alternative)

From Old Galician-Portuguese segundo, from Latin secundus, probably taken as a semi-learned term.

(geometry) second of arc (angle measure)


simplex

en-noun

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.


surface

From French surface. Doublet of superficies.

(mathematics, geometry) The locus of an equation (especially one with exactly two degrees of freedom) in a space of more than two dimensions.

سَطْح

locus of an equation in a more-than-two-dimensional space


homocentric

en-adj

homocentric (comparative more homocentric, superlative most homocentric)

more homocentric (comparative)
most homocentric (superlative)

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

Naturally, there exist three kinds of optical beams: parallel, divergent, and convergent (see Fig. 1.1.1). If a beam, either divergent or convergent, has a single point of intersection of all optical rays it is called a homocentric beam (Fig. 1.1.1b,c). An example of a non-homocentric beam is shown in Fig. 1.1.1 d.

2004, Naftaly Menn, “Geometrical Optics in the Paraxial Area”, in Practical Optics, Burlington, MA: Academic Press, →DOI, →ISBN, page 3:


right triangle

(geometry) A triangle having a right angle as one of its interior angles.

triángulu rectángulu

a triangle having a right angle as one of its interior angles


right-angled triangle

en-noun

right-angled triangle (plural right-angled triangles)


acute-angled triangle

acute-angled triangle (plural acute-angled triangles)


acute triangle

(geometry) A triangle all of the angles of which are acute.


obtuse-angled triangle

obtuse-angled triangle (plural obtuse-angled triangles)


obtuse triangle

obtuse triangle (plural obtuse triangles)

(geometry) A triangle one of whose angles is obtuse.


geometria

pl-noun

geometria f (related adjective geometryczny)

geometryczny (adjective)
geometria (nominative singular)
geometrii (genitive singular)
geometrii (dative singular)
geometrię (accusative singular)
geometrią (instrumental singular)
geometrii (locative singular)
geometrio (singular vocative)


זווית

he-noun

זווית / זָוִית • (zavít) f (plural indefinite זוויות / זָוִיּוֹת, singular construct זווית / זָוִית־, plural construct זוויות / זָוִיּוֹת־)

זָוִית (canonical)
zavít (romanization)
זוויות (indefinite plural)
זָוִיּוֹת (indefinite plural)
זווית (construct singular)
זָוִית־ (construct singular)
זוויות (construct plural)
זָוִיּוֹת־ (construct plural)

Cognate with Aramaic זָוִיתָא and Arabic زاوية (zāwiya).

cog

Aramaic זָוִיתָא


spiral

From Middle French spirale, from Medieval Latin spiralis, from Latin spīra, from Ancient Greek σπεῖρα (speîra, “wreath, coil, twist”).

der

(geometry) A curve that is the locus of a point that rotates about a fixed point while continuously increasing its distance from that point.


spiral

Borrowed from Dutch spiraal (“spiral”), from French spirale, from Medieval Latin spiralis, from Latin spira, from Ancient Greek σπεῖρα (speîra, “wreath, coil, twist”).


folium

en-noun

folium (countable and uncountable, plural foliums or folia)

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

From Latin folium (“leaf”). Doublet of foil and folio, distantly also with phyllo and phyllon.

These circular cubics are Newton's defective hyperbolae, with a diameter, species 39, 41, 45; the ampullate cubic represents the folium of the unipartite quartic, and the ampaniform the bipartite quartic.

1881, Henry M. Jeffery, “On Bicircular Quartics, with a Triple and Double Focus, and Three Single Foci, all of them Collinear.”, in Proceedings of the London Mathematical Society, volume 12, page 22:

I have argued that the real threat the Unruh effect poses to fundamental partical interpretation lies in its suggestion that physically reasonable states outrun the folium of any single irreducible Fock space representation.

2011, Laura Ruetsche, Interpreting Quantum Theories, page 222:

(geometry) A curve of the third order, consisting of two infinite branches having a common asymptote. The curve has a double point, and a leaf-shaped loop.


folium

foliumuri (plural)
folium (accusative indefinite nominative singular)
foliumul (accusative definite nominative singular)
foliumuri (accusative indefinite nominative plural)
foliumurile (accusative definite nominative plural)
folium (indefinite singular)
foliumului (definite singular)
foliumuri (indefinite plural)
foliumurilor (definite plural)
foliumule (singular vocative)
foliumurilor (plural vocative)


evolution

evolution (countable and uncountable, plural evolutions)

extinction

antonym(s) of “survival through adaptation”

/ɛvəˈlʉːʃən/

Borrowed from Latin ēvolūtiō, ēvolūtiōnis (“the act of unrolling, unfolding or opening (of a book)”), from ēvolūtus, perfect passive participle of ēvolvō (“unroll, unfold”), from ex + volvō (“roll”).
Compare typologically Czech vývoj, Serbo-Croatian развој, Russian разви́ть (razvítʹ), развива́ть (razvivátʹ), разви́ться (razvítʹsja), развива́ться (razvivátʹsja), Russian разви́тие (razvítije), related to Proto-Slavic *viti (whence Czech vít, Russian вить (vitʹ)).

تَطَوُّر

general: a gradual process of development

(geometry) The opening out of a curve; now more generally, the gradual transformation of a curve by a change of the conditions generating it.


sphère

sphères (plural)
sphære (alternative archaic)

From Late Latin sphēra, from Latin sphaera (“ball, globe, celestial sphere”), from Ancient Greek σφαῖρα (sphaîra, “ball, globe”). Replaced Old French espere, from the same Latin source.


aire

Inherited from Old French aire, eire, from Latin ārea. Doublet of are and area, which were learned borrowings.

une aire


eccentric

eccentrics (plural)
eccentrick (alternative)
excentric (alternative)
excentrick (alternative)

From Middle French excentrique, from Medieval Latin eccentricus, from Ancient Greek ἔκκεντρος (ékkentros, “not having the earth as the center of an orbit”), from ἐκ (ek, “out”) + κέντρον (kéntron, “point”). Equivalent to ex- + -centric.

der

(geometry, astronomy) A circle not having the same centre as another.


kula

kulka (diminutive)
kula (nominative singular)
kule (nominative plural)
kuli (genitive singular)
kul (genitive plural)
kuli (genitive plural)
kuli (dative singular)
kulom (dative plural)
kulę (accusative singular)
kule (accusative plural)
kulą (instrumental singular)
kulami (instrumental plural)
kuli (locative singular)
kulach (locative plural)
kulo (singular vocative)
kule (plural vocative)

→ Belarusian: ку́ля (kúlja)

desc

→ Russian: пу́ля (púlja) (with sound changes)

→ Ukrainian: ку́ля (kúlja)

Apparently borrowed from Middle High German kūle. In most senses cognate with German Kugel, in the sense “crutch” cognate with German Keule.


circumference

From Latin circumferentia, from circum (“around”) + ferō (“I carry”). Displaced native Old English ymbgang.

(geometry) The line that bounds a circle or other two-dimensional figure.

مُحِيط

line that bounds a circle or other two-dimensional object


tesseract

tesseracts (plural)
tessaract (alternative)

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

From tessara- (“four-”) + Ancient Greek ἀκτίς (aktís, “ray”).

af

Hence the cube determined by these axes is the face of the tesseract which we now have before us.

1906, Charles Howard Hinton, The Fourth Dimension, S. Sonnenschein & Company, page 239:

[…]then it would trace out a higher cube, or tesseract, and each of the six surrounding cubes, carried on in the same motion, would trace tesseracts also,[…].

1910, Henry Parker Manning, The Fourth Dimension Simply Explained, Munn, Incorporated, page 93:

(mathematics, geometry) The four-dimensional analogue of a cube; a 4D polytope bounded by eight cubes (analogously to the way a cube is bounded by six squares).


polytope

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

From German Polytop, equivalent to poly- (“many”) + -tope (“surface”). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.

As is well known, the theory of linear inequalities is closely related to the study of convex polytopes.

1964, Victor Klee, On the Number of Vertices of a Convex Polytope: Canadian Journal of Mathematics, volume XVI, number 4, page 701:

This polytope is mapped into a Cartesian force polytope (resp. torque polytope) in the Cartesian space. Such a polytope represents the exact force (resp. torque) that can be produced on the vehicle main body.

1998, F. Pierrot, M. Benoit, P. Dauchez, “SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles”, in Jadran Lenar I, Manfred L. Husty, editors, Advances in Robot Kinematics: Analysis and Control, page 220:

Verify the Hirsch conjecture for the 3-cube, 4-cube and any other polytope that takes your fancy.
The Steinitz theorem is a very satisfactory understanding of the graphs of three-dimensional polytopes.

2006, Rekha R. Thomas, Lectures in Geometric Combinatorics, page 27:

(geometry) A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence "point, line segment, polygon, polyhedron, ...".


hypercube

(geometry) A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent of a cube for any non-negative integer n.

(geometry) Such a figure in four dimensions; a tesseract.


four-dimensional

(algebraic geometry) Having four dimensions; being measurable along four mutually perpendicular axes.


transversal

From Middle French transversal, from Medieval Latin trānsversālis, from Latin trānsversus.

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:

A line which traverses or intersects any system of other lines transversely.

(geometry) A line intersecting a pair of parallel lines.


transversal

From Medieval Latin trānsversālis, from Latin trānsversus.


trapezium

en-noun

trapezium (plural trapeziums or trapezia)

Recorded since 1570, learned borrowing from Late Latin trapezium, from Ancient Greek τραπέζιον (trapézion, “irregular quadrilateral”, literally “a little table”), diminutive of τράπεζα (trápeza, “table”). Doublet of trapeze.

uder

(geometry, British, Australia, New Zealand) A quadrilateral with two sides parallel.

(restrictively) A quadrilateral with two sides parallel and two sides non-parallel.

(geometry, US, dated) A four-sided polygon with no parallel sides and no sides equal; a simple convex irregular quadrilateral.

مُنْحَرِف

polygon with no parallel sides and no equal sides

trapezoid

four-sided polygon with two parallel sides

trapezoid

four-sided polygon with no sides parallel and no equal sides


trapezium

nl-noun

trapezium n (plural trapeziums or trapezia, diminutive trapeziumpje n)

trapeziums (plural)
trapezia (plural)
trapeziumpje (diminutive neuter)

Borrowed from Late Latin trapezium, from Ancient Greek τραπέζιον (trapézion, “irregular quadrilateral”), diminutive of τράπεζα (trápeza, “table”).

der

(geometry) a trapezium, trapezoid, a quadrilateral with two sides parallel


perverse

LL-Q1860 (eng)-Mélange a trois-perverse.wav

From Middle English perverse, pervers, from Old French pervers, from Latin perversum (“thoroughly turned”), past participle of pervertere, from per- (“thoroughly”) + vertere (“to turn”).

If two antipodal points move continuously on the sphere, they trace out what are called symmetric figures. These figures have corresponding elements equal, and are equal in area, but are not in general superposable. The one is, in fact, the perverse of the other.

1884, Robert Edgar Allardice, Spherical Geometry:

(geometry) A chiral opposite of something; a mirror image with opposite handedness.


acutangular

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


axle

From Middle English axil, in turn a combination of Old English eax and Old Norse ǫxull.

Axle in the Encyclopædia Britannica (11th edition, 1911)

the Sun’s axle


lieu

→ English: lieu

Inherited from Middle French lieu, from Old French leu, from Latin locum, from Old Latin stlocus, from Proto-Indo-European *stel- (“to put, place, locate”).

(geometry) locus (set of all points whose location satisfies or is determined by one or more specified conditions)


y-axis

independent variable
independent variable

(algebraic geometry) The axis on a graph that is usually drawn from bottom to top and usually shows the range of values of variable dependent on one other variable, or the second of two independent variables.


z-axis

(algebraic geometry) The axis on a graph of at least three dimensions that is usually drawn vertically and usually shows the range of values of a variable dependent on two other variables or the third independent variable.

z-as

axis on a graph that is usually drawn vertically


hoof

From Middle English hoof, hof, from Old English hōf, from Proto-Germanic *hōfaz (compare West Frisian hoef, Dutch hoef, German Huf, Danish hov, Norwegian hov, Swedish hov), from Proto-Indo-European *ḱoph₂ós (compare Sanskrit शफ (śaphá, “hoof, claw”), Avestan 𐬯𐬀𐬟𐬀 (safa, “hoof”), possibly Czech, Polish kopyto).


skeleton

skeletons (plural)
skeleta (plural)
sceleton (alternative)

From New Latin sceleton, from Ancient Greek σκελετόν (skeletón), the neuter of σκελετός (skeletós, “dried up, withered, dried body, parched, mummy”), from σκέλλω (skéllō, “dry, dry up, make dry, parch”), from Proto-Indo-European *(s)kelh₁- (“to parch, wither”); compare Ancient Greek σκληρός (sklērós, “hard”).

(geometry) The vertices and edges of a polyhedron, taken collectively.

luuranko

geometry: vertices and edges of a polyhedron


discriminant

(geometry) The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pⁿ⁻¹ is singular.


Cartesian coordinate

en-noun

Cartesian coordinate (plural Cartesian coordinates)

Cartesian coordinates (plural)
Cartesian (alternative)
coördinate (alternative)
Cartesian (alternative)
co-ordinate (alternative)

(geometry) The coordinates of a point measured from an origin along a horizontal axis from left to right (the x-axis) and along a vertical axis from bottom to top (the y-axis). This can be extended to three-dimensions by the z-axis perpendicular to the x- and y-axes.


Cartesian coordinates

perpendicular distance
perpendicular distance

(algebraic geometry) The coordinates of a point measured as its perpendicular distance to the right of a vertical axis (the y-axis) and its perpendicular distance above a horizontal axis (the x-axis).


Euclidean distance

Euclidean distance (countable and uncountable, plural Euclidean distances)

Euclidean distances (plural)
euclidean distance (alternative)

euklidinen etäisyys

(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:

The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:
 d( textbf a, textbf b)=√


Cartesian distance

Cartesian distance (plural Cartesian distances)

Cartesian distances (plural)
cartesian distance (alternative)

(algebraic geometry) Euclidean distance.


diameter

diameters (plural)
diametre (alternative dated nonstandard)

From Old French diametre (French diamètre), from Latin diametrus, from Ancient Greek διάμετρος (diámetros) (γραμμή (grammḗ)) (diametros grammē, “line measuring across”), from διά (diá, “across”) + μέτρον (métron, “measure”). By surface analysis, dia- + -meter.

(geometry) Any straight line between two points on the circumference of a circle that passes through the centre/center of the circle; a chord that passes through the center of the circle.

In cases without good face contact, the diameter of the toolholder at the front of the flange or the tool itself should not be any larger than the gage diameter of the toolholder shank from a bending stiffness viewpoint.

2005, David A. Stephenson, John S. Agapiou, Metal Cutting Theory and Practice, page 280:

Viable non-malformed singleton pregnancies were selected for cerebellar measurements; transcerebellar diameter, (TCD), left and right cerebellar diameters (LCD, RCD).

2015 October 23, “Periconception Maternal Folate Status and Human Embryonic Cerebellum Growth Trajectories: The Rotterdam Predict Study”, in PLOS ONE, →DOI:

(geometry) The maximum distance between any two points in a metric space.


diameter

diamètêr (canonical)
diameter-diameter (plural)

From Dutch diameter, from French diamètre, from Latin diametrus, from Ancient Greek διάμετρος (diámetros).


diameter

diameter (indefinite nominative singular)
diameters (genitive indefinite singular)
diametern (definite nominative singular)
diameterns (definite genitive singular)
diametrar (indefinite nominative plural)
diametrars (genitive indefinite plural)
diametrarna (definite nominative plural)
diametrarnas (definite genitive plural)


oblique

From Middle French oblique, from Latin oblīquus (also spelled oblīcus) (“slanting, sideways, indirect, envious”).


kite

kites (plural)
kight (alternative)
kyte (alternative)

The noun is from Middle English kyte, kīte, kete (“a kite endemic to Europe, especially the red kite (Milvus milvus)”), from Old English cȳta (“kite; bittern”), from Proto-West Germanic *kūtijō, diminutive of Proto-Germanic *kūts (“bird of prey”), from Proto-Indo-European *gewH-d- (“to cry, screech”). The English word is cognate with Scots kyt, kyte (“kite; bird of prey”), Middle High German kiuzelīn, kützlīn (“owling”) (modern German Kauz (“owl”)). Possibly a doublet of coot.
Sense 3 (“lightweight toy”) is from the fact that it hovers in the air like the bird.
The verb is derived from the noun.

der

A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. Note that a parallelogram has opposite congruent sides, whereas the congruent sides of kites are adjacent. Therefore, a kite is also a parallelogram only when both pairs of adjacent congruent sides of the kite are congruent to each other, making the kite a rhombus.

2011, W. Michael Kelley, “Quadrilaterals”, in The Humongous Book of Geometry Problems: Translated for People Who Don’t Speak Math!!, New York, N.Y.: Alpha Books, →ISBN, page 216:

(geometry) A polygon resembling the shape of a traditional toy kite (sense 3): a quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end.

鷂形 /鹞形

geometry: a polygon resembling the shape of a traditional toy kite; a quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end


section

From secar + -ion, alternatively from Latin sectiō.


normal

en-adj

normal (comparative normaler or more normal, superlative normalest or most normal)

normaler (comparative)
more normal (comparative)
normalest (superlative)
most normal (superlative)

From Latin normālis (“made according to a carpenter's square; later: according to a rule”), from nōrma (“carpenter's square”), of uncertain origin; doublet of normale. The earliest meaning of the word in English was "perpendicular; forming a right angle" like something normālis (“made according to a carpenter's square”), but by Late Latin normālis had also come to mean "according to a rule", from which modern English senses of the word derive: in the 1800s, as people began to quantitatively study things like height, weight and blood pressure, the usual or most common values came to be called "normal", and by extension values regarded as healthy or desirable came to be called "normal" regardless of their usuality.

der

According to norms or rules or to a regular pattern.

(mathematics) Adhering to or being what is considered natural or regular in a particular field or context:

(algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.

The interior normal vector of a perfect sphere always point toward the center, and the exterior normal vector directly away, and both are always collinear with the ray whose tip ends at the point of intersection, which is the intersection of all three sets of points.

(geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.


normal

en-noun

normal (countable and uncountable, plural normals)

(geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.

նորմալ

mathematics: a line perpendicular to another


normal

head

normal m (genitive singular normail, nominative plural normail)

normail (genitive singular)
normail (nominative plural)
normal (indefinite nominative singular)
normail (indefinite nominative plural)
a normail (indefinite singular vocative)
a normala (indefinite plural vocative)
normail (genitive indefinite singular)
normal (genitive indefinite plural)
normal (dative indefinite singular)
normail (dative indefinite plural)
an normal (definite nominative singular)
na normail (definite nominative plural)
an normail (definite genitive singular)
na normal (definite genitive plural)
leis an normal (dative definite singular)
don normal (dative definite singular)
leis na normail (dative definite plural)

/ˈn̪ˠɔɾˠ(ə)mˠəlˠ/

(geometry, statistics, chemistry) normal


normal

Learned borrowing from Latin normālis. By surface analysis, norma + -al.

(geometry) normal (perpendicular to a tangent of a curve or derivative of a surface)


normal

es-adj

normal m or f (masculine and feminine plural normales)


normal

normal (indefinite nominative singular)
normals (genitive indefinite singular)
normalen (definite nominative singular)
normalens (definite genitive singular)
normaler (indefinite nominative plural)
normalers (genitive indefinite plural)
normalerna (definite nominative plural)
normalernas (definite genitive plural)

From Latin nōrmālis, from nōrma + -ālis, equivalent to norm + -al.

(geometry) a normal (a line which is perpendicular to another line or to a surface)


affinity

en-noun

affinity (countable and uncountable, plural affinities)

From Middle English affinite, from Old French affinité. Ostensibly equivalent to affine + -ity.

(geometry) An automorphism of affine space.