quindecagon

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


enneagon

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


undecagon

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


decagon

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


heptagon

Since 16th century, from Ancient Greek ἑπτάγωνον (heptágōnon), from ἑπτά (heptá, “seven”) + γωνία (gōnía, “angle”). Equivalent to hepta- + -gon.

A polygon with seven sides and seven angles.


nonagon

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


dodecagon

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


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.

der

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


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


pole

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

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


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.


atlas

Borrowed from Latin Atlas, from the name of the Ancient Greek mythological figure Ἄτλας (Átlas, “Bearer (of the Heavens)”), from τλῆναι (tlênai, “to suffer”, “to endure”, “to bear”). The sense referring to books of maps comes from the Atlas of Mercator, which he named thus in honor of Atlas, who was supposed to be skillful in astronomy and the doctrine of the sphere. The sense referring to the vertebra reflects that the spine carries the globe of the cranium (the neck carries the head).

differential geometry
differential geometry

(differential geometry, topology) A family of coordinate charts that cover a manifold.

atlas

(differential geometry, topology) family of coordinate maps that cover a manifold


proper

en-adj

proper (comparative more proper, superlative most proper)

more proper (comparative)
most proper (superlative)

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

(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).


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 is from the noun.

cog

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


sagitta

en-noun

sagitta (plural sagittas or (arrowworm) sagittae)

/səˈd͡ʒɪt.ə/

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.


ellipsis

ellipsis (countable and uncountable, plural ellipses)

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


turn

→ Japanese: ターン (tān)

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

պտույտ

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


net

Etymology tree
Proto-Indo-European *neHd-der.
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.


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.


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.”).
The now dated UK school sense ("division grouping school students") is derived from public school nomenclature, which was later used 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


gradian

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


monotonic

From Ancient Greek μονότονος (monótonos, “monotone”) + -ικός (-ikós, “-ic”), equivalent to monotone + -ic.

suffix

Of or using the Greek system of diacritics which discards the breathings and employs a single accent to indicate stress. It replaced polytonic system in 1982.

μονοτονικός

of or using the Greek system of diacritics which discards the breathings and employs a single accent to indicate stress

independent variable
independent variable

(mathematics) Of a function: that either never decreases or never increases as its independent variable increases.

monoton

mathematics: never decreasing or increasing as its independent variable increases

The Same Spade talk-alike, super-cynical heroine of the piece is named Emma Victor, and there's no end to her rapid-fire, monotonic, street-smart patter.

1988 December 11, Georgia Cotrell, “A Lezbeen Sam Spade”, in Gay Community News, volume 16, number 22, page 8:


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.


log

To multiply two numbers, add their logs.


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


bulk

en-noun

bulk (countable and uncountable, plural bulks)

From Middle English bulk, bolke (“a heap, cargo, hold; heap; bulge”), borrowed from Old Norse búlki (“the freight or the cargo of a ship”), from Proto-Germanic *bulkô (“beam, pile, heap”), from Proto-Indo-European *bʰelǵ- (“beam, pile, prop”). Compare Icelandic búlkast (“to be bulky”), Swedish dialectal bulk (“a bunch”), Danish bulk (“bump, knob”).
Conflated with Middle English bouk (“belly, trunk”).

der

(bodybuilding) Excess body mass, especially muscle.


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


hendecagon

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


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.


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.


alternation

en-noun

alternation (countable and uncountable, plural alternations)

Latin alternatio; compare French alternation.
Morphologically 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.


diamond

diamond (countable and uncountable, plural diamonds)

From Middle English dyamaunt, from Old French diamant, from Late Latin diamas, from Latin adamas, from Ancient Greek ἀδάμας (adámas, “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

Elphingston. Pearl a Chevron Diamond between three Boars Heads Eraz'd Ruby, arm'd of the first. / Eymouth. Diamond a Lyon Rampant Pearl, on a Canton of the 2d, a Cross Ruby.

1720, Francis Nichols, Rudiments of Honour, page 296:

The Field is Ruby, on a Bend Topaz, three Martlets Diamond. The Armes of the most Noble and Puissant Lord, Edward Brabazon, Earl of Meath, and Baron of Atherdee in the Kingdom of Ireland. His Lordship's Atchievements are Quarterly of sixteen Coats. 1. Brabazon, as above. 2. Diamond, on a Chevron between three Pickaxes Pearl, as many Mullets Ruby, by the Name of Mosley. 3. Saphire, ten Bezants, 4, 3, 2, 1, by the Bisset.

1726, John Guillim, The Banner Display'd; Or, an Abridgment of Guillim, page 504:

Pearl, an Eagle, Diamond, between three Crosses Patee, Ruby, for Morrys.

1754, John Lodge, The Peerage of Ireland; Or, a Genealogical History of the ..., page 71:

(heraldry) Sable, when blazoning by precious stones.

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

(geometry) The polyiamond made up of two triangles.

(baseball) The entire field of play used in the game.

The teams met on the diamond.

(baseball) The infield of a baseball field.


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)

From Latin alternō (“take turns”), from alternus (“one after another, by turns”), from alter (“other”) + -rnus. See altern, 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.


chord

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”)

der

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.


cyclic quadrilateral

en-noun

cyclic quadrilateral (plural cyclic quadrilaterals)

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


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.


height

en-noun

height (countable and uncountable, plural heights)

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.
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.


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.


FFT

fast Fourier transform
fast Fourier transform#English

(signal processing) Initialism of fast Fourier transform.


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.


trace

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

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


functional

en-adj

functional (comparative more functional, superlative most functional)

more functional (comparative)
most functional (superlative)

/ˈfʌŋkt͡ʃənəl/


functional

/ˈfʌŋkt͡ʃənəl/

(mathematics, functional analysis) A scalar-valued linear function on a vector space.

(computing) An object encapsulating a function pointer (or equivalent).

関数オブジェクト

an object encapsulating a function pointer


sigmoid

Borrowing from Ancient Greek σῑγμοειδής (sīgmoeidḗs, “of the shape of sigma”), from σῖγμᾰ (sîgma, “sigma”) + -ο- (-o-) + -ειδής (-eidḗs, “-oid, -like”); Equivalent to sigma + -oid. Compare with French sigmoïde.

af

(archaic) Semi-circular, like the uncial or lunar sigma (similar to English C).

Curved in two directions, like the letter "S", or the Greek ς (sigma); having a serpentine shape.

(mathematics) Exhibiting logistic growth; having a graph that accelerates until it reaches a carrying capacity.

(anatomy) Relating to the sigmoid colon.


sigmoid

If we had the textbook from a hundred years in the future that contains all the simple ideas that actually work, that take so long to identify in practice — the ReLUs instead of sigmoids — for those of us who’ve been following AI for, like, more than the last couple of years and know what I’m taking about there.

2023 June 29th, “AI will kill all of us | Eliezer Yudkowsky interview” (16:12–16:28 from the start), in The David Pakman Show, spoken by Eliezer Yudkowsky, via YouTube:

sigmoid function
sigmoid function#English

(mathematics) Ellipsis of sigmoid function.


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


Platonic solid

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)


octahedron

en-noun

octahedron (plural octahedra or octahedrons)

From Ancient Greek ὀκτώ (oktṓ, “eight”) + ἕδρα (hédra, “seat”).

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


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.

der

(countable, zoology) The cutting region of the crown of an upper molar, usually the anterior part.


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.

կողմ

The cup is right on the edge of the table.

He is standing on the edge of a precipice.

Here by, upon the edge of yonder coppice; / A stand, where you may make the fairest shoot.

c. 1595–1596 (date written), William Shakespeare, “Loues Labour’s Lost”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act IV, scene i]:

In worst extremes, and on the perilous edge / Of battle when it rag'd, in all assaults

1667, John Milton, “(please specify the page number)”, in Paradise Lost. […], London: […] [Samuel Simmons], and are to be sold by Peter Parker […]; [a]nd by Robert Boulter […]; [a]nd Matthias Walker, […], →OCLC; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873, →OCLC:

they never wanted the pretext, and seldom the will, to harass and pursue, even to the very edge of destruction, any of their less powerful neighbours

1819 December 20 (indicated as 1820), Walter Scott, Ivanhoe; a Romance. […], volume (please specify |volume=I to III), Edinburgh: […] Archibald Constable and Co.; London: Hurst, Robinson, and Co. […], →OCLC:

A sharp terminating border; a margin; a brink; an extreme verge.

ръб

any sharp terminating border; a margin; a brink; extreme verge

in the edge of evening

supposing that the new general, unacquainted with his army, and on the edge of winter, would not hastily oppose them.

1670, John Milton, The History of Britain, The Prose Works of John Milton, published 1853, Volume V, page 203

The border or part adjacent to the line of division; the beginning or early part (of a period of time)


edge

en-verb

edge (third-person singular simple present edges, present participle edging, simple past and past participle edged)

edges (present singular third-person)
edging (participle present)
edged (participle past)
edged (past)

Near-synonym: goon

Jimmy has been edging for 6 hours straight; is his dick okay?

“I think of it as mine, but, yes, it's his cock I've been edging with. Do you edge?”

2011, Nicholson Baker, House of Holes, page 181:

His mouth was open and he was still jerking his dick. Justin knew he must have been edging by then.

2012, Ryan Field, Field of Dreams: The Very Best Stories of Ryan Field, page 44:

“I'm going to edge you all night long. That should take the sass out of you.”

2016, Jenna Jacob, Lured By My Master: (The Doms of Genesis, Book 6):

(intransitive, transitive, slang) To intentionally stay or keep someone extremely close to the point of orgasm for a long period of time.


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.

медиана

geometry: line segment joining vertex and midpoint of opposing side


-hedron

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

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


-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.


knot

From Middle English knotte, from Old English cnotta, from Proto-West Germanic *knottō, from Proto-Germanic *knuttô, *knudô (“knot”); probably ultimately from Proto-Indo-European *gnod- (“to bind”).
See also Old High German knoto (German Knoten, Dutch knot, Low German Knütte; also Old Norse knútr > Danish knude, Swedish knut, Norwegian knute, Faroese knútur, Icelandic hnútur; also Latin nōdus and its Romance descendants. Doublet of knout, node, and nodus.
* (unit of speed): From the practice of counting the number of knots in the log-line (as it is paid out) in a standard time. Traditionally spaced at one every ¹⁄₁₂₀ of a mile.

A knot can be defined as a non-self-intersecting broken line whose endpoints coincide: when such a knot is constrained to lie in a plane, then it is simply a polygon.

(mathematics) A non-self-intersecting closed curve in (e.g., three-dimensional) space that is an abstraction of a knot (in sense 1 above).


parameter

[pəˈɹæm.ə.ɾɚ]

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.


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

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.


dependent variable

en-noun

dependent variable (plural dependent variables)

In the equation z = x² + y, z is the dependent variable.

(algebra) In an equation, the variable whose value depends on one or more variables in the equation.


independent variable

independent variable (plural independent variables)

Coordinate term: dependent variable

(sciences) The variable that is changed or manipulated in a series of experiments.


cubic curve

(mathematics) A plane curve having the equation y=a.x³+b.x²+c.x+d.


congruence

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


complement

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.


simplex

en-noun

simplex (plural simplexes or simplices or simplicia)

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

Henri Poincaré
Pieter Hendrik Schoute
Simplex (disambiguation)
simplex

From Latin simplex (“simple”).
In the mathematical sense, apparently first used (in German) in 1902, Pieter Hendrik Schoute, Mehrdimensionale Geometrie, where Schoute first suggests the term Simplicissimum, but then from the next page decides to use simplex "for short". In his pioneering works on algebraic topology, Henri Poincaré had previously introduced the concept, but not the actual term simplex.

linearly independent
linearly independent

(geometry, algebraic topology) An analogue in a space of arbitrary dimensionality of the triangle or tetrahedron; the convex hull of n+1 linearly independent points in n-dimensional space; in other words, the triangle, tetrahedron etc., generalized to an arbitrary number of dimensions.

单纯形

an analogue in any dimension of the triangle or tetrahedron


homocentric

en-adj

homocentric (comparative more homocentric, superlative most homocentric)

more homocentric (comparative)
most homocentric (superlative)

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:


acute-angled triangle

en-noun

acute-angled triangle (plural acute-angled triangles)


right-angled triangle

right-angled triangle (plural right-angled triangles)


obtuse-angled triangle

obtuse-angled triangle (plural obtuse-angled triangles)


acute triangle

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


right triangle

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

pravoúhlý trojúhelník

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


obtuse triangle

obtuse triangle (plural obtuse triangles)

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


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.”).
Doublet of terminus and termon. Old English had termen, from the same source.

член

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.


chart

→ Japanese: チャート (chāto)

→ Korean: 차트 (chateu)

→ Swahili: chati

→ Welsh: siart

Borrowed from Middle French charte (“card, map”), from Late Latin charta (“paper, card, map”), Latin charta (“papyrus, writing”), from Ancient Greek χάρτης (khártēs, “papyrus, thin sheet”). See charter, card, carte.

der

coordinate chart
coordinate chart#English

(differential geometry, topology) Synonym of coordinate chart.


surface

From French surface. Doublet of superficies.

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

سَطْح

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


bijection

PIE word
 *dwóh₁
From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.

2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214:

Note in particular that a function is a bijection if and only if it's both an injection and a surjection.

2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167:

The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.

2013, William F. Basener, Topology and Its Applications, unnumbered page:

(set theory) A one-to-one correspondence, a function which is both a surjection and an injection.

Nicolas Bourbaki
bijection
Éléments de mathématique

funció bijectiva

function that is both a surjection and an injection


surjection

/sɜː(ɹ)ˈd͡ʒɛk.ʃən/

From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.
Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).

bor

In some special cases, however, the number of surjections A#x5C;rightarrowB can be identified.

1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220:

Let J#x3D;#x5C;cap#x5F;im#x5F;i be the (irredundant) primary decomposition of J. We associate to the pair (J,#x5C;omega) the element #x5C;textstyle#x5C;sum#x5F;i(m#x5F;i,#x5C;omega#x5F;i)#x5C;inG, where #x5C;omega#x5F;i is the equivalence class of surjections from L#x2F;m#x5F;iL#x5C;oplus(A#x2F;m#x5F;i)#x7B;n-1#x7D; to m#x5F;i#x2F;m#x5F;i² induced by #x5C;omega.

1999, M. Pavaman Murthy, “A survey of obstruction theory for projective modules of top rank”, in Tsit-Yuen Lam, Andy R. Magid, editors, Algebra, K-theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday, American Mathematical Society, page 168:

In Banach space theory, a mapping u#x3A;E#x5C;rightarrowF (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isometric isomorphism. Moreover, by the classical open mapping theorem, u is a surjection iff the associated mapping from E#x2F;#x5C;text#x7B;ker#x7D;(u) to F is an isomorphism.

2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43:

(set theory) A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y.

Nicolas Bourbaki
Surjective function
Éléments de mathématique


cap

Inherited from Middle English cappe, from Old English cæppe, 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.


folium

en-noun

folium (countable and uncountable, plural foliums or folia)

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.


transformation

transformation (countable and uncountable, plural transformations)

Borrowed from Middle French, from Ecclesiastical Latin trānsfōrmātiō.
Morphologically transform + -ation

(mathematics) The replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system.


transform

From Middle English transformen, from Old French transformer, from Latin transformo, transformare, from trans (“across”, preposition) + forma (“form”).

(geology, seismology) A transform fault.


n-dimensional

(mathematics) Having an arbitrary number of dimensions.


polytope

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, polygon, polyhedron, ...".


tesseract

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).

"I shall just sit down for a moment and pop on my boots and then I'll be on my way. Speaking of ways, pet, by the way, there is such a thing as a tesseract."

1962, Madeleine L'Engle, A Wrinkle in Time, published 2019, unnumbered page:

(science fiction) Any of various fictional mechanisms that explain extradimensional, superluminal, or time travel outside the geometry of the physical universe.


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.


evolution

en-noun

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”).

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.


unit interval

The unit interval of a signal with a baud rate of 1,000 Bd is 1 millisecond.

symbol duration time
symbol duration time

(telecommunications) symbol duration time.


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.

شِبْهُ مُنْحَرِفٍ

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

A region on the ventral side of the brain, either just back of the pons Varolii, or, as in man, covered by the posterior extension of its transverse fibers.


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.


eccentric

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.


spiral

From Middle French spirale, from Medieval Latin spiralis, from Latin spira, from Ancient Greek σπείρα (speíra, “wreath, coil, twist”).

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


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


trajectory

/tɹəˈd͡ʒɛktəɹi/

From New Latin trāiectōria f (“trajectory”) (used by Newton), the feminine of trāiectōrius (“of or pertaining to throwing across”), from Latin trāiectus (“thrown over or across”), past participle of trāiciō, from trans- (“across, beyond”) (see trans-) + iaciō (“to throw”) (from Proto-Indo-European *(H)yeh₁- (“to throw, impel”)). Middle French and Middle English had trajectorie (“end of a funnel”), from Latin trāiectōrium.

(cybernetics) The ordered set of intermediate states assumed by a dynamical system as a result of time evolution.


y-axis

(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


axial

(ornithology) A flight feather that appears between the primaries and secondaries on some birds.


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.


apoapsis

en-noun

apoapsis (plural apoapsides or apoapsises or apoapses)

apoapsides (plural)
apoapsises (plural)
apoapses (plural)

(astronomy) The point of a body's elliptical orbit about the system's centre of mass where the distance between the body and the centre of mass is at its maximum.


periapsis

periapsis (plural periapsides or periapsises or periapses)

periapsides (plural)
periapsises (plural)
periapses (plural)

1983, Richard O. Fimmel, Laurence Colin, Eric Burgess, Pioneer Venus, NASA SP-461, page 109,
Figure 5-19. Sun-Venus-Orbiter geometry illustrates how the periapsis moves around the planet during the Venusian sidereal year to sample day and night hemispheres. Because the planet rotates in a retrograde direction, it takes more than one Venusian sidereal year for periapsis to move over all longitudes of the planet (as explained in text).

We don't always want to burn near periapsis. Suppose we want to change the height at periapsis. The most efficient place to change the radius of periapsis is at apoapsis. Consider applying #x5C;Deltav at some other point in the orbit. In this case both periapsis and apoapsis will change. If we apply the #x5C;Deltav tangentially at apoapsis, all of the #x5C;Deltav will go into changing periapsis, and vice versa.

2001, D. A. Vallado, Fundamentals of Astrodynamics and Applications, Springer, page 325:

2004, R. S. Saunders, et al., Mars Odyssey Mission, C. T. Russell (editor), 2001 Mars Odyssey, Kluwer Academic Publishers, page 34,
The main aerobraking phase began once the point of the spacecraft's periapsis had been lowered to within 110 km above the Martian surface.

(astronomy, astrophysics) The point of a body's (elliptical) orbit in a 2-body gravitational system such that the distance between the two bodies (measured from their respective centres of mass) is at its minimum.


Cartesian coordinate

Cartesian coordinate (plural Cartesian coordinates)

(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).


Cartesian distance

Cartesian distance (plural Cartesian distances)

(algebraic geometry) Euclidean distance.


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


Euclidean distance

Euclidean distance (countable and uncountable, plural Euclidean distances)

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)=√


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.


asymptote

circa 1650, from Ancient Greek ἀσύμπτωτη (asúmptōtē), the feminine of Apollonius Pergaeus' (circa 200 BC) Ancient Greek adjective ἀσύμπτωτος (asúmptōtos, “not falling together”), from ἀ- (a-, “not”) + συν- (sun-, “together”) + πτωτός (ptōtós, “fallen”).

af

mathematical analysis
mathematical analysis

(mathematical analysis) A straight line which a curve approaches arbitrarily closely as it goes to infinity. The limit of the curve; its tangent "at infinity".

asintota

a straight line which a curve approaches arbitrarily closely


asymptote

en-verb

asymptote (third-person singular simple present asymptotes, present participle asymptoting, simple past and past participle asymptoted)

asymptotes (present singular third-person)
asymptoting (participle present)
asymptoted (participle past)
asymptoted (past)

2006: Neil deGrasse Tyson, The Perimeter of Ignorance
As you become more scientific, yes, the religiosity drops off, but it asymptotes.

(mathematical analysis) To approach, but never quite touch, a straight line, as something goes to infinity.


perturbation

en-noun

perturbation (countable and uncountable, plural perturbations)

Borrowed from Middle French perturbation, from Old French perturbacion, from Latin perturbatio.

Natures that haue much Heat, and great and violent deſires and Perturbations, are not ripe for Action, till they haue paſſed the Meridian of their yeares: As it was with Iulius Cæſar, and Septimius Seuerus.

1625, Francis [Bacon], “Of Youth and Age. XLII.”, in The Essayes […], 3rd edition, London: […] Iohn Haviland for Hanna Barret, →OCLC, pages 247–248:

(countable) A small change in a physical system, or more broadly any definable system (such as a biological or economic system)

perturbo

a small change in a physical system or any definable system


Euler's totient function

Named after Swiss mathematician Leonhard Euler (1707–1783).

named-after

(number theory) The function that calculates the total number of integers below a given integer that are coprime to it.


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).


diameter

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”).

(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.

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


oblique

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


skeleton

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”).

der

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

luuranko

geometry: vertices and edges of a polyhedron


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.


integral

Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.

(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;

(mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.


pentagram

From Ancient Greek πεντάγραμμον (pentágrammon), noun form of the adjectives πεντάγραμμος (pentágrammos) and πεντέγραμμος (pentégrammos, “five-lined, having five lines”). Equivalent to penta- + -gram.

der

πεντάγραμμον

Prove that the circles so belonging to the 6 pentagrams formed by 6 lines meet in a point, and so on; the series of theorems being interminable.

1871, W. J. C. Miller, editor, Mathematical Questions and Solutions, volume XV, page 47:

The passive pentagrams of spirit are drawn first in the quarters of the passive elements—water and earth—and likewise followed by the appropriate traditional elemental pentagram.

2007, Christopher Penczak, The Temple of High Witchcraft: Ceremonies, Spheres, and the Witches' Qabalah, page 345:

Four figures involve 12 pentagrams arranged as in the faces of a dodecahedron with their vertices touching.

2012, John Barnes, Gems of Geometry, page 59:

The shape of a five-pointed star constructed of five intersecting lines meeting at the vertices, such that a central pentagon and five surrounding isosceles triangles are formed; often with magical connotations; a 5/2 (or 5/3) star polygon.


acnode

(geometry) An isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve.


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 use of the word in English was to mean "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 and weight and blood pressure, the usual or most common values came to be referred to as "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 an ideal perfect sphere will always point toward the center, and the exterior normal vector directly away, and both will always be co-linear 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) A line or vector that is perpendicular to another line, surface, or plane.

նորմալ

mathematics: a line perpendicular to another


kite

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.

leko

military aviation, slang: aircraft — see also aircraft

leija

sailing, slang: spinnaker — see also spinnaker

Four-sided figures without parallel sides include trapezoids and kites.

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

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


lituus

(geometry) A curve with polar equation r²θ=a², where a is a constant.


roll

en-verb

roll (third-person singular simple present rolls, present participle rolling, simple past and past participle rolled)

rolls (present singular third-person)
rolling (participle present)
rolled (participle past)
rolled (past)

From Middle English rollen, partly from Old French roller, roler, röeler, röoler, from Medieval Latin rotulāre (“to roll; to revolve”), from Latin rotula (“a little wheel”), diminutive of rota (“a wheel”); partly from Anglo-Latin rollāre, from the same ultimate source.

rol

to cause something to revolve by turning over and over

rol

to move, or cause to be moved, upon rollers or small wheels

(geometry) To apply (one line or surface) to another without slipping; to bring all the parts of (one line or surface) into successive contact with another, in such a manner that at every instant the parts that have been in contact are equal.

rol

geometry: to apply (one line or surface) to another without slipping


eigenfunction

For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.

2000, John von Neumann, E. Wigner, “On the Behaviour of Eigenvalues in Adiabatic Processes”, in Hinne Hettema, transl., edited by Hinne Hettema, Quantum Chemistry: Classic Scientific Papers, World Scientific, published 1929, page 25:

Problems that require an investigation of eigenvalues and eigenfunctions arise in connection with numerous topics in mechanics, the theory of vibrations and stability, hydrodynamics, elasticity, acoustics, electrodynamics, quantum mechanics, etc.

2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications, CRC Press (Chapman & Hall), page 1:

(mathematics) A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue).


salient

en-adj

salient (comparative more salient, superlative most salient)

more salient (comparative)
most salient (superlative)

The heraldic sense “leaping” and the sense “projecting outward” are borrowed from Latin salientem, the accusative form of saliēns (“springing, leaping”), present participle of saliō (“leap, spring”, verb). The senses “prominent” and “pertinent” are relatively recent, and derive from the phrase salient point, which is a calque of the Latin punctum saliēns, a translation of Aristotle's term for the embryonal heart visible in (opened) eggs, which he thought seemed to move already. Compare also the German calque der springende Punkt.

(geometry) Denoting any angle less than two right angles.


regular tessellation

en-noun

regular tessellation (plural regular tessellations)

(geometry) A tessellation of the plane by a convex regular polygon.

Mathworld article on regular tessellation


semiregular tessellation

semiregular tessellation (plural semiregular tessellations)

(geometry) A tessellation of the plane by two or more different convex regular polygons.


ambigram

From ambi- + -gram. Coined by Douglas Hofstadter in 1983-1984.

Two nonvisual factors provide dissymmetry and prevent the ambigram from existing in a static equilibrium; most of the letters in an ambigram metamorphose into other letters when reversed; and each of those accompanying sentences provides a different idea of the word's meaning.

1992, John Langdon, Wordplay, published 2005, page 52:

1997, Research and Education Networking, Volume 8, Issues 1-6, page 290,
An ambigram is a word that reads the same right-side-up and upside-down. MOW is a natural ambigram, for instance, but any word can be flipped if the right graphic artist gets his hands on it.

Next, I imagine that Switch #2 causes me every single weekend (and every other spare moment as well) to elect, instead of designing ambigrams or working hard on my book about being a strange loop, to spend hours on end watching professional football games on a huge-screen television and delightedly ogling all the busty babes in the beer ads.

2007, Douglas Hofstadter, I Am a Strange Loop, page 312:

A calligraphic design that may be read as the same word or phrase (or sometimes different words or phrases) when oriented in two different ways, usually when reflected along a vertical or horizontal axis or when rotated through 180 degrees.

Indiana University Bloomington
Merriam-Webster
ambigram

雙面語

design that reads as the same word or phrase in two different orientations


tessellate

en-verb

tessellate (third-person singular simple present tessellates, present participle tessellating, simple past and past participle tessellated)

tessellates (present singular third-person)
tessellating (participle present)
tessellated (participle past)
tessellated (past)

Etymology tree
Proto-Indo-European *kʷetwóres
Proto-Hellenic *kʷétwores
Ancient Greek τέσσαρες (téssares)bor.
Latin tessera
Proto-Indo-European *-lós
Proto-Italic *-elos
Latin -lus
Latin tessella
Latin -ātus
Latin tessellātuslbor.
English tessellate
Learned borrowing from Latin tessellātus, from tessella, diminutive of tessera; from Ancient Greek τέσσαρες (téssares), from Proto-Indo-European *kʷetwóres.

tessellieren

to completely fill with multiple copies of a two-dimensional shape edge to edge

Regular hexagons tessellate.

(intransitive, geometry) to cover a two-dimensional shape, such that multiple copies of itself placed edge to edge cover an area leaving no space between the shapes.

It is possible to tessellate the plane with equilateral triangles and regular hexagons.

(transitive, geometry) To completely fill (an area) when multiple copies of one or more two-dimensional shapes are placed edge to edge.


disk

→ Japanese: ディスク (disuku)

→ Korean: 디스크 (diseukeu)

→ Norwegian Bokmål: disk

→ Thai: ดิสก์ (dìt)

→ Turkish: disk

→ Welsh: disg

From Ancient Greek δίσκος (dískos, “a circular plate suited for hurling”), from δικέω (dikéō, “to hurl, to launch”). Doublet of dais, desk, disc, discus, dish, and diskos.

doublet

He still uses disks from 1979.

(computer hardware) Ellipsis of floppy disk.

(computer hardware) Ellipsis of hard disk.

She burned some disks yesterday to back up her computer.

(computer hardware, nonstandard) An optical disc, such as a LaserDisc, CD, DVD, Blu-ray, or similar removable optical storage medium.

(botany) A ring- or cup-shaped enlargement of the flower receptacle or ovary that bears nectar or, less commonly, the stamens.


tomahawk

From an Eastern Algonquian word, most likely Powhatan tumahák; compare also Malecite-Passamaquoddy tomhikon (“ax”), Abenaki temahigan, demahigan (“ax”).

(geometry) A geometric construction consisting of a semicircle and two line segments that serves as a tool for trisecting an angle; so called from its resemblance to the American Indian axe.


orthogonal

/ɔːˈθɒɡ.ə.nəl/

/ɔɹˈθɑɡ.ə.nəl/

By surface analysis, ortho- + -gon + -al. From French orthogonal, in turn from Medieval Latin orthogōnālis and Latin orthogōnius (“right-angled”), ultimately from Ancient Greek ὀρθογώνιος (orthogṓnios, “rectangular”).

der

A chord and the radius that bisects it are orthogonal.

(geometry) Of two objects, at right angles; perpendicular to each other.


conics

That branch of geometry which treats of the cone and the curves which arise from its sections.


bisect

en-verb

bisect (third-person singular simple present bisects, present participle bisecting, simple past and past participle bisected)

bisects (present singular third-person)
bisecting (participle present)
bisected (participle past)
bisected (past)

From bi- (“bi-, two”) + Latin secāre (“to cut”).

affix

(transitive) To cut or divide into two parts.

(transitive, geometry) To divide an angle, line segment, or other figure into two equal parts.

puolittaa

geometry: to divide an angle, line segment or other figure into two equal parts


bisect

(geometry) A bisector, which divides into two equal parts.


affine

en-adj

affine (comparative more affine, superlative most affine)

more affine (comparative)
most affine (superlative)

Now, let P, Q, and R be three noncollinear points that are left fixed by an affine transformation T.

1986, Patrick J. Ryan, Euclidean and Non-Euclidean Geometry: An Analytic Approach, Cambridge University Press, page 44:

In our example of the affine cryptosystem family, deciphering is also accomplished by an affine map, namely P#x5C;equiva#x7B;-1#x7D;C-a#x7B;-1#x7D;b#x5C;bmodN, and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair (a#x7B;-1#x7D;,-a#x7B;-1#x7D;b).

1987, Neal Koblitz, A Course in Number Theory and Cryptography, Springer, page 81:

Clearly every linear functional is affine, and every affine function is both convex and concave.

2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 256:

linear transformation
linear transformation

(not comparable, geometry) Of or pertaining to a function expressible as f(⃑x)=A⃑x+⃑b (where A is a linear transformation and ⃑b is a constant), which, regarded as a transformation, maps parallel lines to parallel lines and finite points to finite points.

仿射

pertaining to a kind of function that generalises a linear transformation


circular

circular (comparative more circular, superlative most circular)

more circular (comparative)
most circular (superlative)

From Middle English circuler, circuleer, circulere, from Old French circulier, from Late Latin circularis, from Latin circulus, diminutive of circus (“ring”).

Here, in the transept and choir, where the service was being held, one was conscious every moment of an increasing brightness; colours glowing vividly beneath the circular chandeliers, and the rows of small lights on the choristers' desks flashed and sparkled in front of the boys' faces, deep linen collars, and red neckbands.

1918, W[illiam] B[abington] Maxwell, chapter V, in The Mirror and the Lamp, Indianapolis, Ind.: The Bobbs-Merrill Company, →OCLC:


cusp

From Latin cuspis (“a point, spear, pointed end”); first used in astrology.

bor

(geometry) A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.

cúspide

point of a curve where it has no tangent


focal

Learned borrowing from New Latin focālis. By surface analysis, focus + -al.

lbor

Again, if the plane of the impressed couple intersects the mean plane between N and C, it will envelope the cone whose focals are ON, ON′, and whose internal axis is therefore OA.

1877, James Booth, A Treatise on Some New Geometrical Methods, page 209:

(geometry, obsolete) One of two lines perpendicular to the axis of a cone such that the cosine of the angle between the line and the axis is equal to the ratio of the cosines o the semiangles of the cone.


octant

(geometry) The eighth part of a disc; a sector of 45 degrees; half a quadrant.


toroid

(mathematics) A surface generated by a closed curve (especially a circle) rotating about, but not intersecting or containing, an axis in its own plane.


mitre

From Middle English mytre, from Old French mitre, from Ancient Greek μίτρα (mítra, “headband, turban”). Its use in reference to a counterfeit coin derived from the bishop's mitre stamped upon it. Doublet of Mithras, Mithra, Mitra, and Mehr.

doublet

(geometry, rare) A square with one triangular quarter missing from the outside.


spline

Mid-1700s East Anglian dialect. Origin uncertain but perhaps from Old Danish splind or North Frisian splinj and ultimately related to the root of splinter.

(mathematics, computing) Any of a number of smooth curves used to join points.


oblique circle

(projection) a circle whose plane is oblique to the axis of the primitive plane


septic

Enriques states that it is possible to construct a family of septics with a singular curve of degree 7 and genus 4 having a triple point that degenerates to the above configuration[…].

2002, Ingrid C. Bauer, Fabrizio Catanese, Roberto Pignatelli, “Canonical Rings of Surfaces Whose Canonical System has Base Points”, in Ingrid C. Bauer et al., editors, Complex Geometry: Collection of Papers Dedicated to Hans Grauert, page 66:

Now consider the two septics C = U⁷ᵢ₌₁Cᵢ, D = U⁷ᵢ₌₁Dᵢ and note that for i = 1,2,3,4,5,6 the lines Cᵢ and Dᵢ are parallel, so that the intersection of two septics S' consists of 6⁶^([sic]) + 6 + 1 = 43 points and it is the singular set of a foliation of degree 6.

2003, Antonio Campillo, Santiago Encinas, “Two Dimensional Complete Ideals”, in Luchezar L. Avramov et al., editors, Commutative Algebra: Interactions with Algebraic Geometry: International Conference, page 71:

(mathematics) A mathematical object (function, curve, surface, etc.) of degree seven.


oblique line

(geometry) A line that, meeting or tending to meet another, makes oblique angles with it.


oblique system of coordinates

(analytic geometry) A system in which the coordinate axes are oblique to each other.


secant

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

From Latin secāns, present participle of secō (“to cut”).

(geometry) A straight line that intersects a curve at two or more points.

(trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec


elation

en-noun

elation (countable and uncountable, plural elations)

From Middle English elacioun, from Old French elacion, from Latin ēlātiōnem, accusative singular of ēlātiō (“exaltation, elevation; pride, elation”), from ēlātus, perfect passive participle of efferō (“bring forth or out; raise; exalt”), from ē (“out of”), short form of ex, + ferō (“carry, bear”).

(geometry) A collineation that fixes all points on a line (called its axis) and all lines though a point on the axis (called its center).


gyration

gyration (countable and uncountable, plural gyrations)

/ˌd͡ʒaɪˈɹeɪʃ(ə)n/

From gyre (“to spin around; to gyrate, to whirl; (rare) to make (something) spin or whirl around; to spin, to whirl”) + -ation (suffix indicating actions or processes). Gyre is from Late Middle English giren (“to turn (something) away; to cause (something) to revolve or rotate; to travel in a circle”), from Old French girer (“to turn”), and directly from its etymon Latin gȳrāre, the present active infinitive of gȳrō (“to turn in a circle, rotate; to circle or revolve around”) (from gȳrus (“circle; circular motion; circuit, course”), from Ancient Greek γῦρος (gûros, “a circle, a ring”), from Proto-Indo-European *gew- (“to bend; to curve”)) + -ō (suffix forming regular first-conjugation verbs).

ĝirado

act of turning or whirling, especially around a fixed axis or centre — see also rotation

(also figuratively) The act of turning or whirling, especially around a fixed axis or centre; a circular or spiral motion; rotation.

(specifically, Euclidean geometry) A rotation around an axis which is not the centre of rotational symmetry; an eccentric or off-centre rotation.


equator

From Late Latin (circulus) aequator (diei et noctis).

bor

Baishui is about as close to the equator as Tampa, Florida.

2018, VOA Learning English > China's Melting Glacier Brings Visitors, Adds to Climate Concerns:

(geography, often “the Equator”) An imaginary great circle around Earth, equidistant from the two poles, and dividing earth's surface into the northern and southern hemisphere.

(astronomy) A similar great circle on any sphere, especially on a celestial body, or on other reasonably symmetrical three-dimensional body.

Slice the onion through the equator.

The midline of any generally spherical object, such as a fruit or vegetable, that has identifiable poles.


exceptional

en-adj

exceptional (comparative more exceptional, superlative most exceptional)

more exceptional (comparative)
most exceptional (superlative)

ordinary

antonym(s) of “superior due to exception or rarity”

an exceptional curve; an exceptional divisor

(geometry) Corresponding to something of lower dimension under a birational correspondence.


node

→ Irish: nód

From Middle English node, borrowed from Latin nōdus. Doublet of knot, knout, and nodus.

(geometry) The point at which a curve crosses itself, being a double point of the curve. See crunode and acnode.

duaalipiste

geometry: point at which a curve crosses itself

(geometry) A similar point on a surface, where there is more than one tangent-plane.


meander

From Latin Maeander, from Ancient Greek Μαίανδρος (Maíandros) – a river in Asia Minor (present day Turkey) known for its winding course (modern Turkish Menderes).

(mathematics) A self-avoiding closed curve which intersects a line a number of times.


primitive

From Middle English primitif, from Old French primitif, from Latin prīmitīvus (“first or earliest of its kind”), from prīmus (“first”); see prime. Doublet of primitivo.

der

(mathematics) A function whose derivative is a given function; an antiderivative.


roulette

en-noun

roulette (countable and uncountable, plural roulettes)

Borrowed from French roulette (“roulette, little wheel”). The sense "situation with a random chance of incurring serious harm" may be abstracted from Russian roulette.

bor

(countable, geometry) The locus of a point on a plane curve that rolls without slipping along another fixed plane curve.


spire

(geometry) The part of a spiral generated in one revolution of the straight line about the pole.


trapeze

From French trapèze, from Latin trapezium. Doublet of trapezium.


nonic

(algebraic geometry) Describing a curve the equation of which is nonic.


sine wave

(trigonometry, signal processing) A periodically oscillating waveform as described by the sine function, possibly multiplied by some amplitude, shifted by some phase, and translated by an additive constant.


trope

Japanese: トロープ (torōpu)

Korean: 트로프 (teuropeu)

From Latin tropus, from Ancient Greek τρόπος (trópos, “a manner, style, turn, way; a trope or figure of speech; a mode in music; a mode or mood in logic”), related to τροπή (tropḗ, “solstice; trope; turn”) and τρέπειν (trépein, “to turn”); compare turn of phrase. The verb is derived from the noun.

der

Hence the section must be a conic passing through six nodes, that is, the plane touches the surface all along a conic, and is therefore a trope. The complete section of the surface by a trope is a conic counted twice; since this passes through six nodes, the trope must touch the six quadric tangent cones along generators which are tangents to the singular conic.

1905, R[onald] W[illiam] H[enry] T[urnbull] Hudson, “The Quartic Surface”, in Kummer’s Quartic Surface, Cambridge: At the University Press, →OCLC; republished Cambridge: Cambridge University Press, 2001, →ISBN, page 15:

A tangent space meeting a quartic surface in a conic.

troop

music, Roman Catholicism: phrase or verse added to the Mass

I take account of conical and biplanar nodes, or, as I call them, cnicnodes, and binodes; of pinch-points on the nodal curve; and of close-points and off-points on the cuspidal curve: viz. I assume that there are / C, cnicnodes, / B, binodes, / j, pinch-points, / #x5C;chi, close points, / #x5C;theta, off-points, / deferring for the present the explanation of these singularities. The same letters, accented, refer to the reciprocal singularities. Or using "trope" as the reciprocal term to node, these will be / C', cnictropes, / B', bitropes, / j', pinch-planes, / #x5C;chi', close-planes, / #x5C;theta', off-planes; / but these present themselves, not in the equations above referred to, but in the reciprocal equations.

1868 November 12, [Arthur] Cayley, “VI. A Memoir on the Theory of Reciprocal Surfaces”, in Philosophical Transactions of the Royal Society of London, volume 159, part I, London: Printed by Taylor and Francis, Red Lion Court, Fleet Street, published 1869, →OCLC, page 202:

(archaic) The reciprocal of a node on a surface.

Mathematical senses.
The reciprocal of a node on a surface.


arccosine

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the cosine function.


arcsine

/ˈɑːɹkˌsaɪn/

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the sine function. Symbol: arcsin, sin⁻¹


equilateral triangle

en-noun

equilateral triangle (plural equilateral triangles)

(geometry) A triangle having all three sides equal.


isosceles triangle

isosceles triangle (plural isosceles triangles)

(geometry) A triangle having at least two sides equal.


hypotenuse

From Latin hypotenusa, from Ancient Greek ὑποτείνουσα πλευρά (hupoteínousa pleurá, “side subtending [the right angle]”), from ὑποτείνουσα (hupoteínousa, “stretching, extending, subtending”), active participle of ὑποτείνω (hupoteínō, “subtend, stretch under”).

uder

ὑποτείνουσα πλευρά

Coordinate term: cathetus

(geometry) The side of a right triangle opposite the right angle.

وَتَر

the side of a right triangle opposite the right angle


transition function

en-noun

transition function (plural transition functions)

If (U#x5F;1,#x5C;psi#x5F;1) and (U#x5F;2,#x5C;psi#x5F;2) are two complex charts, then the transition function is #x5C;psi#x5F;#x7B;12#x7D;#x3A;#x5C;psi#x5F;1(U#x5F;1#x5C;capU#x5F;2)#x5C;rightarrow#x5C;psi#x5F;2(U#x5F;1#x5C;capU#x5F;2), given by #x5C;psi#x5F;#x7B;12#x7D;#x3D;#x5C;psi#x5F;2#x5C;circ#x5C;psi#x5F;1#x7B;-1#x7D;. We say M is a complex manifold if it has an atlas of complex charts (U,#x5C;psi), such that all the transition functions are holomorphic, as maps from #x5C;mathbb#x7B;C#x7D;ᵐ to itself.

2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics), Oxford University Press, →ISBN, →LCCN, page 76:

(differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed.

transitiokuvaus

homeomorphism between subsets of images of overlapping coordinate charts


TMI

TMI (countable and uncountable, plural TMIs)

(organic chemistry) Initialism of trimethylindium.

transmarginal inhibition
transmarginal inhibition#English

(psychology) Initialism of transmarginal inhibition.

trans-Mars injection
trans-Mars injection#English

(astrodynamics) Initialism of trans-Mars injection.


hypercomplex number

hypercomplex number (plural hypercomplex numbers)

(mathematics) Any of several types of extended complex number, consisting of a real part and two or more imaginary parts (each a real multiple of a distinct square root of −1), which may be imagined as a point in a multi-dimensional space.


indivisible

PIE word
 *dwóh₁
From Middle French indivisible, from Late Latin indivisibilis.

(geometry) An infinitely small quantity which is assumed to admit of no further division.


variety

variety (countable and uncountable, plural varieties)

From Middle French varieté (“variety”) (modern French variété (“variety; genre, type”)) or directly from its etymon Latin varietās (“difference; diversity, variety”) + English -ty (suffix forming abstract nouns from adjectives). Varietās is derived from varius (“different, diverse, various; variegated”) (possibly ultimately from Proto-Indo-European *h₁weh₂- (“to abandon; to give out; to leave”)) + -tās (suffix forming feminine abstract nouns indicating a state of being). The English word displaced the native Old English mislīcnes.
Sense 1.3.2 (“total number of distinct states of a system; logarithm to the base 2 of the total number of distinct states of a system”) was coined by the English psychiatrist William Ross Ashby (1903–1972) in his work An Introduction to Cybernetics (1956).
cognates
* Galician variedade (“variety”)
* Italian varietà (“difference; variety”)
* Portuguese variedade (“variety”)
* Spanish variedad (“breed; variety”)

der

A collection or number of different things.

(algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).

algebraic variety
algebraic variety#English


equivalent

en-adj

equivalent (comparative more equivalent, superlative most equivalent)

more equivalent (comparative)
most equivalent (superlative)

From equi- + -valent.
From Latin aequivalentem, accusative singular of aequivalēns, present active participle of aequivaleō (“I am equivalent, have equal power”).

A square may be equivalent to a triangle.

(geometry) Equal in measure but not admitting of superposition; applied to magnitudes.


factorial

The expression #x7B;#x7D;#x5F;nC#x5F;r means the number of combinations of n things taken r at a time. It is also written #x5C;binomnr, and is equal to#x5C;frac#x7B;n(n-1)(n-2)(n-3)#x5C;cdots#x5C;cdots(n-r#x2B;1)#x7D;#x7B;r#x21;#x7D;or n#x21;#x2F;r#x21;(n-r)#x21;, in which r#x21; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inclusive.

1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428:

This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;1.2.3#x5C;cdotsn.But what does this equal?
Well, of course we can say that it is equal to n factorial and write#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;n#x21; and then use our calculators, but inventing a new symbol like 'factorial' feels like an admission of defeat!

2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School, volume 47, number 4, page 40:

(mathematics, combinatorics) The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.


locus

A circle is the locus of points from which the distance to the center is a given value, the radius.

(mathematics) The set of all points whose coordinates satisfy a given equation or condition.

轨迹

set of all points given by an equation or condition


bell curve

→ Turkish: çan eğrisi (calque)

All this is enhanced by well-chosen illustrations: the bell curve of Galton and similar frequency-curves,[…]

(mathematics) The bell-shaped curve that is typical of the normal distribution.

Gaussova křivka

bell shaped curve typical of the normal distribution

Gaußkurve

strictly the PDF of a normal distribution


norm

From Latin norma (“a carpenter's square, a rule, a pattern, a precept”). Doublet of norma.

norm

math: function that maps vectors to non-negative reals

(mathematics) A function which satisfies a particular set of formal conditions, created to generalize the notion of the length of a vector. Formally, a real-valued function on a vector space, generally denoted v↦|v| or v↦‖v‖, that satisfies the following properties:

given a scalar k, ‖kv‖=|k|·‖v‖, where |k| is the absolute value of k;

given two vectors v,w, ‖v+w‖<‖v‖+‖w‖ (the triangle inequality).


concentric

en-adj

concentric (comparative more concentric, superlative most concentric)

more concentric (comparative)
most concentric (superlative)

Japanese: コンセント (konsento)

Korean: 콘센트 (konsenteu)

From Middle English concentrik, from Middle French concentrique, from Medieval Latin concentricus, from Latin con- (“with, together”) + centrum (“circle, center”). Equivalent to con- + -centric.

Seven huge concentric semi-circular rings of stone surround the northern end, and quite rightly are Grade 2-listed by conservation body Historic England.

2020 August 26, Tim Dunn, “Great railway bores of our time!”, in Rail, page 45:


geometry

en-noun

geometry (countable and uncountable, plural geometries)

From Middle English gemetry, geometrie, from Old French geometrie (modern French géométrie), from Latin geōmetria, from Ancient Greek γεωμετρία (geōmetría, “geometry, land-survey”), from γεωμέτρης (geōmétrēs, “land measurer”), from γῆ (gê, “earth, land, country”) + -μετρία (-metría, “measurement”), from μέτρον (métron, “a measure”). By surface analysis, geo- + -metry. Doublet of gematria.

der

(algebraic geometry, countable) A mathematical object comprising representations of a space and of its spatial relationships.


noble

en-adj

noble (comparative nobler or more noble, superlative noblest or most noble)

nobler (comparative)
more noble (comparative)
noblest (superlative)
most noble (superlative)

From Middle English, from Old French noble, from Latin nōbilis (“knowable, known, well-known, famous, celebrated, high-born, of noble birth, excellent”), from nōscere, gnōscere (“to know”).
False cognate of Arabic نبيل (nabīl). Displaced native Middle English athel, from Old English æþele.

der

(geometry, of a polyhedron) Both isohedral and isogonal.


concave

en-adj

concave (comparative more concave, superlative most concave)

more concave (comparative)
most concave (superlative)

From Middle English concave, from Old French concave, from Latin concavus.

(geometry, not comparable, of a polygon) Not convex; having at least one internal angle greater than 180 degrees.


convex

convex (comparative more convex, superlative most convex)

more convex (comparative)
most convex (superlative)

Borrowed from Middle French convexe, from Latin convexus (“arched”).

(geometry, not comparable, of a polygon) having no internal angles greater than 180 degrees.


parallelogram

/ˌpæ.ɹə.ˈlɛl.ə.ˌɡɹæm/

From Latin parallelogrammum, from Ancient Greek παράλληλος (parállēlos, “parallel”) + γραμμή (grammḗ, “line”).

uder

(geometry) A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.


grade

→ Japanese: グレード (gurēdo)

→ Swahili: gredi

Borrowed from Middle French grade (“a grade, degree”), from Latin gradus (“a step, pace, degree”), from Proto-Italic *graðus, from Proto-Indo-European *gʰradʰ-, *gʰredʰ- (“to walk, go”). Doublet of gradus.
Cognate with Gothic 𐌲𐍂𐌹𐌸𐍃 (griþs, “step, grade”), Bavarian Gritt (“step, stride”), Lithuanian grìdiju (“to go, wander”).

(geometry) In a linear system of divisors on an n-dimensional variety, the number of free intersection points of n generic divisors.

aste

geometry: number of free intersection points of n generic divisors


conic section

(geometry) Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola and hyperbola.


construction

en-noun

construction (countable and uncountable, plural constructions)

→ Mongolian: констракшн (konstrakšn)

From Middle English construccioun, construction, from Old French construction, from Latin cōnstructiō, from cōnstruere, present active infinitive of cōnstruō.
Morphologically construct + -ion.

(geometry) A geometric figure of arcs and line segments that is drawable with a straightedge and compass.


PDF

PDF (countable and uncountable, plural PDFs)

Translingual: .pdf

probability density function
probability density function

(probability theory) Alternative letter-case form of pdf (“probability density function”)


swastika

swastika (countable and uncountable, plural swastikas)

Learned borrowing from Sanskrit स्वस्तिक (svastika), from सु- (su-, “good, well”) + अस्ति (asti), a verbal abstract of the root of the verb "to be", स्वस्ति (svasti) thus meaning "well-being" — and the diminutive suffix क (ka); hence "little thing associated with well-being", corresponding roughly to "lucky charm". First attestation in English in 1871, a Sanskritism that replaced the Grecian term gammadion. From 1932 onwards it often referred specifically to the version used by the National Socialist German Workers’ Party (also called the "hooked cross", or German Hakenkreuz).

sauwastika

left-facing; symbolizing the night or the tantric aspects of Kali

This was signed by Dana Da, who added pentacles and pentagrams, and a crux ansata, and half-a-dozen swastikas, and a Triple Tau to his name, just to show that he was all he laid claim to be.

1888, Rudyard Kipling, “The Sending of Dana Da”, in In Black and White, Folio Society, published 2005, pages 423–4:

It is clear from archaeological finds that they enjoyed wearing Christian crosses, though they might enliven these with such symbols as the Indian swastika which Buddhists had brought them.

2009, Diarmaid MacCulloch, A History of Christianity, Penguin, published 2010, page 270:

(countable) A cross with arms of equal length all bent halfway along at a 90° angle to the right or to the left, used as a religious symbol by various ancient and modern civilizations, but now mainly seen and used in the West (with arms angled to the right) as a symbol of Nazism and fascism.

swastika

a cross with arms of equal length all bent halfway along at a 90° angle


proportional

It is almost superfluous to remark that the numbers attached to the elements of compounds are those of the proportionals in which they combine […]

1828, William Thomas Brande, Tables in Illustration of the Theory of Definite Proportionals, page xiii:

(mathematics, geometry, archaic) A proportion.


two-dimensional

a two-dimensional character in a play

Not creating the illusion of depth; lacking detail or believability.


three-dimensional

en-adj

three-dimensional (not generally comparable, comparative more three-dimensional, superlative most three-dimensional)

more three-dimensional (comparative)
most three-dimensional (superlative)

A good novel needs three-dimensional characters.


arc-

From Latin arcus (“bow, arc”), as they represent an angle or arc. Compare etymology of arch.

arkusz-

forms the names of inverse trigonometric and hyperbolic functions

(mathematics, sometimes proscribed) Alternative form of ar- used to form the names of inverse trigonometric functions, and the symbols for these functions.


helix

From Latin helix, from Ancient Greek ἕλιξ (hélix, “something twisted or spiral”).

der

(mathematics) A curve on the surface of a cylinder or cone such that its angle to a plane perpendicular to the axis is constant; the three-dimensional curve seen in a screw or a spiral staircase.


ellipse

From French ellipse. Doublet of ellipsis.

(geometry) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.


solid of revolution

en-noun

solid of revolution (plural solids of revolution)

A cylinder is a solid of revolution generated by rotating a rectangle about one of its axes.

A solid produced by taking a particular two-dimensional curve and rotating it through 360° about an axis. The curve will sweep out a surface, and the region inside the surface defines a solid.

omdrejningslegeme

solid produced rotating a two-dimensional curve through 360° about an axis


parabola

parabola (plural parabolas or parabolae or parabolæ)

parabolas (plural)
parabolae (plural)
parabolæ (plural)

Borrowed from New Latin parabola, from Ancient Greek παραβολή (parabolḗ), from παραβάλλω (parabállō, “I set side by side”), from παρά (pará, “beside”) + βάλλω (bállō, “I throw”). Doublet of parable, parole, and palaver.

(geometry) The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix).


radiant

From Middle English radyant, from Latin radiāns, radiantis, present participle of radiāre (“to emit rays or beams”).

(geometry) A straight line proceeding from a given point, or fixed pole, about which it is conceived to revolve.


spheroid

UFOs are reported as being either oblate (saucer-shaped) or prolate (cigar-shaped) spheroids.

A solid of revolution generated by rotating an ellipse about its major (prolate), or minor (oblate) axis.


similitude

similitude (countable and uncountable, plural similitudes)

From Old French similitude. By surface analysis, similar + -itude.

(countable, geometry) A similarity: a transformation of Euclidean space that preserves angles and the ratios of distances.