radial

en-adj

radial (comparative more radial, superlative most radial)

more radial (comparative)
most radial (superlative)

From Medieval Latin radiālis (“radial”), from Latin radius.

What is the relationship between arc length and radial length?

(geometry) Of, or relating to a radius (line joining to a geometric centre).

radial velocity


superellipse

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(algebra, geometry) a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t


superellipsoid

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(algebra, geometry) A closed surface, of which the sphere and ellipsoid are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t, z = c.cos^(2/r)t.


radical center

(geometry) A point at which the radical lines of three circles meet.


facultative

facultative (comparative more facultative, superlative most facultative)

more facultative (comparative)
most facultative (superlative)

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From French facultatif. By surface analysis, faculty + -ative.

For then it is seen, as before, that it is the points outside the two sheets which are facultative, and not the points between the surface and the touching plane.

1866, George Salmon, Lessons Introductory to the Modern Higher Algebra, Dublin: Hodges, Smith, and Co., page 197:

(geometry, of a point) At which a given function is positive.


gon

From Ancient Greek γωνία (gōnía, “angle”). More in Wikipedia at gradian § History and name.

(geometry, trigonometry) One hundredth of a right angle: a gradian.

goniometry and other derivatives of gonio-


agonic

International Geomagnetic Reference Field

From Ancient Greek ᾰ̓- (ă-, the alpha privativum, a prefix forming words having a sense opposite to the word or stem to which it is attached) + γωνία (gōnía, “angle”) + -ic.


quadrature of the circle

(geometry) The problem, proposed by ancient Greek geometers, of using a finite ruler-and-compass construction to make a square with the same area as a given circle.


point cloud

A series of points in three-dimensional space that collectively describe the geometry of a physical object.


involute

involutes (plural)
involuted (alternative)

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(geometry) A curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object.

involuutta

a curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object


solidity

en-noun

solidity (countable and uncountable, plural solidities)

From solid + -ity, from Middle French solidité, from Latin soliditās.

(geometry) The solid contents of a body; volume; amount of enclosed space.


equilateral

Kissinger had wanted to keep an “equilateral” distance between the US, USSR and China. Under Carter, they became de facto partners.

2025 April 12, Edward Luce, “The revenge of geopolitics”, in FT Weekend, Life & Arts, page 2:

(geometry, of a polygon) Having all the sides equal.

ewesydig

referring to a polygon all of whose sides are of equal length

(geometry, of a polyhedron) Having all the faces equal.


equiangular

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æquiangular (alternative archaic)
equangular (alternative)

(geometry) Of a polygon, having all interior angles equal. This is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square.

роўнаку́тны

geometry: having all internal angles equal


regular polygon

regular polygon (plural regular polygons)

(geometry) A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).


interior angle

(geometry) The inner angle between two sides of a polygon.


Cartesian plane

From the name of the French mathematician and philosopher René Descartes who is credited with developing the mathematics.

(geometry) A coordinate plane, with an applied Cartesian coordinate system.

karteesinen taso

coordinate plane with Cartesian coordinates


rhombicosidodecahedron

rhombicosidodecahedron (plural rhombicosidodecahedra or rhombicosidodecahedrons)

rhombicosidodecahedra (plural)
rhombicosidodecahedrons (plural)

/ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹən/

/ˌɹɒmbaɪˌkəʊsidəʊˌdɛkəˈhiːdɹə/

PIE word
 *déḱm̥
Etymology tree
New Latin rhombicosidodecaēdronlbor.
English rhombicosidodecahedron
Learned borrowing from New Latin rhombicosidodecaēdron (coined by the German astronomer and mathematician Johannes Kepler (1571–1630) in his work Harmonices Mundi Libri V (The Harmony of the World in Five Books, 1619)), a blend of Latin rhomb(us) + īcos(aedron) + -i- + dodecaēdron. The English word is analysable as a blend of rhomb(ic) + icosidodecahedron, referring to the fact that the 30 square faces lie in the same planes as the 30 rhombic faces of the rhombic triacontahedron, which is dual to the icosidodecahedron.

coinage

Archimedean solid, one of the thirteen solids described by Archimedes, which, without being regular, have all their solid angles alike, all their faces regular, and not less than four faces of any one kind; […] They are […] the rhombicosidodecahedron, the truncated icosidodecahedron, and the snub-dodecahedron.

1889, “Archimedean, a.”, in William Dwight Whitney, editor, The Century Dictionary: An Encyclopedic Lexicon of the English Language […], volume I, New York, N.Y.: The Century Co., →OCLC, page 297, column 1:

The purpose of this article is to offer a method of approach for investigating the stellation pattern of the deltoidal hexecontahedron, the dual of the rhombicosidodecahedron.

1989, P. W. Messer, M[agnus] J[oseph] Wenninger, “Symmetry and Polyhedral Stellation—II”, in Computers & Mathematics with Applications, volume 17, numbers 1–3, Oxford, Oxfordshire: Pergamon Press, →DOI, →ISSN, →OCLC, page 195; reprinted in István Hargittai, editor, Symmetry 2: Unifying Human Understanding (International Series in Modern Applied Mathematics and Computer Science; 18), Oxford, Oxfordshire: Pergamon Press, 1989, →ISBN, part 1, page 195:

There are two distinct rhombicosidodecahedra, one bearing the unmodified name and the other called the great rhombicosidodecahedron. Like the rhombus, the icosahedron and the dodecahedron, all of the great rhombicosidodecahedron’s 62 faces are either [square] rhombi (30), equilateral triangles (20) or regular pentagons (12).

1994, Steven Schwartzman, “rhombicosidodecahedron”, in The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: 2:Mathematical Association of America, →DOI, →ISBN, page 189, column 1:

Next, the totality of 31 axes is illustrated in a rhombicosidodecahedron, an Archimedean solid composed of 30 squares, 20 triangles, and 12 pentagons[…], with a view to the inside of the model showing the center of the group, the point of invariancy O […] Finally, the other dihedral subgroups are also illustrated on a rhombicosidodecahedron: D#95;3 of order 6 and index 10 […] and D#95;5 of order 10 and index 6[…].

1996, Hugo F[rançois] Verheyen, “Groups of Isometries”, in Symmetry Orbits (Design Science Collection), Boston, Mass.; Basel, Basel-Stadt: Birkhäuser, →DOI, →ISBN, part I (Realization of Symmetry Groups), page 37:

[…] I noticed that the little balls (rhombicosidodecahedrons) had openings shaped in the form of triangles, rectangles, and pentagons.

2014, Thomasenia Lott Adams, Joanne LaFramenta, “Conclusion”, in Math Know-how: Answers to Your Most Persistent Teaching Issues, Grades 3–5, Thousand Oaks, Calif.; London: Corwin, SAGE Publications, →ISBN, page 172:

(geometry) An Archimedean solid with 62 regular faces (20 triangles, 30 squares, and 12 pentagons), 60 vertices and 120 edges.

斜方二十・十二面体

しゃほうにじゅうじゅうにめんたい

菱形二十・十二面体

りょうけいにじゅうじゅうにめんたい

小菱形二十・十二面体

しょうりょうけいにじゅうじゅうにめんたい

切頂菱形三十面体

せっちょうりょうけいさんじゅうめんたい


circularly

en-adv

circularly (comparative more circularly, superlative most circularly)

more circularly (comparative)
most circularly (superlative)

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From Middle English circulerlich, equivalent to circular + -ly.


Johnson solid

From Johnson (“a surname”) + solid, after American mathematician Norman Johnson, who listed them in 1966.

1986 April, Andrew Hume, Folding Regular Polyhedra, AUUGN: Australian Unix Users Group Newsletter, Volume 6, Number 5, page 40,
The Johnson solids, combined with the Archimedean polyhedra and five of the regular polyhedra, constitute all the possible convex polyhedra with regular faces..])

There are other possible models that we have not written about and for which we do not include pictures. namely the Johnson solids and their truncations [2]. (The egg^([truncated hexadecahedron]) is an approximation of a truncation of a Johnson solid.)

2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 2:

Students will be very unlikely to discover very many of the Johnson solids on their own. Someone may come up with the triangular and pentagonal dipyramids, but the others are just not very intuitive. Once students are convinced that there are no other possibilities than the ones they've come up with, then it is time to unveil some of the more complicated Johnson solids.

2012, Thomas Hull, Project Origami: Activities for Exploring Mathematics, 2nd edition, page 159:

(geometry) Any of a class of convex polyhedra that have regular faces but are not uniform (that is, not Platonic solids, Archimedean solids, prisms, or antiprisms).

solido di Johnson

convex non-uniform polyhedron that has regular faces


Archimedean solid

en-noun

Archimedean solid (plural Archimedean solids)

Named after ancient Greek mathematician and engineer Archimedes of Syracuse (c. 287 – c. 212 BCE).

(geometry) Any of a class of convex semiregular polyhedra, composed of two or more types of regular polygon meeting in identical vertices.

sòlid arquimedià

any of a class of semi-regular convex polyhedra composed of two or more types of regular polygon meeting in identical vertices


DMS

DMS (countable and uncountable, plural DMSs)

(uncountable, geometry) Initialism of Degree-Minute-Second (a method of writing angles).


polyacron

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From Ancient Greek πολῠ- (polŭ-) and ᾰ̓́κρον (ắkron).


Cartesian product

Cartesian product (plural Cartesian products)

Cartesian products (plural)
cartesian product (alternative)

From Cartesian + product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept.

On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way.

1987, M. Göckeler, T. Schücker, Differential Geometry, Gauge Theories, and Gravity, published 1989, page 98:

(geometry, of an m-dimensional space X and an n-dimensional space Y) An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y.


bisector

South Street is the bisector of Broken Dreams Boulevard.

(geometry) A line or curve that bisects or divides a line segment, angle, or other figure into two equal parts.


developable surface

developable surface (plural developable surfaces)

(geometry) A surface (in more than two dimensions, a plane is trivially developable) that can be flattened into a plane without distortion.


straight line

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(geometry) A line with no curvature; a line with constant direction. The path of shortest length between two points.


funicular

en-adj

funicular (comparative more funicular, superlative most funicular)

more funicular (comparative)
most funicular (superlative)

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From Latin fūniculus (“cord”), diminutive from fūnis (“cord”) + -culus.


spherical geometry

en-noun

spherical geometry (usually uncountable, plural spherical geometries)

The basic concepts of Euclidean geometry of the plane are the point and the (straight) line; in spherical geometry, the corresponding concepts are the point and the great circle.

Due to the way the geometry of a sphere's surface differs from that of the plane, spherical geometry has some features of a non-Euclidean geometry and is sometimes described as being one. Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.

1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,
Spherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans.

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

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

To collect the boundary of the point set in the tree we pass a bounding box (for Euclidean geometries) or the universal set (for spherical geometries) to the root of the tree.

2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272:

2020, Marshall A. Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,
It has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum.

(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;

The geometry of the 2-dimensional surface of a sphere;
(countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.


noneuclidean geometry

noneuclidean geometry (countable and uncountable, plural noneuclidean geometries)

non-Euclidean geometry
non-Euclidean geometry#English

(geometry, US) Alternative form of non-Euclidean geometry.


spherical cap

(geometry) A portion of the surface of a sphere cut off by a plane.


spherical lune

(geometry) A portion of the surface of a sphere cut off by two vertical planes through the centre of the sphere.


spherical wedge

spherical wedge (plural spherical wedges)

(geometry) A volume of a sphere lying between two vertical planes through the centre of the sphere.


touchpoint

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The Gergonne triangle is defined by the three touchpoints of the incircle on the three sides.


orthocenter

orthocenters (plural)
orthocentre (alternative)

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(geometry) The intersection of the three lines that can be drawn flowing from the three corners of a triangle to a point along the opposite side where each line intersects that side at a 90 degree angle; in an acute triangle, it is inside the triangle; in an obtuse triangle, it is outside the triangle.


Lemoine hexagon

Lemoine hexagon (plural Lemoine hexagons)

Named after the French mathematician Émile Lemoine.

(geometry) A cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.

Mathworld article on the Lemoine hexagon


heptahedron

heptahedron (plural heptahedrons or heptahedra)

heptahedrons (plural)
heptahedra (plural)

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(geometry) A polyhedron with seven faces.


zero-dimensional

(geometry) Having zero dimensions; having no extent in any direction.


chiliagon

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From Ancient Greek χιλιάγωνος (khiliágōnos), from χίλιοι (khílioi, “thousand”) + γωνία (gōnía, “angle”). Equivalent to chilia- + -gon.

If Kant's claim is just that it is impossible to have a sensory experience of the absence of space, then by contrast it is not impossible to have a sensory experience of a chiliagon.

1995, Lorne Falkenstein, Kant's Intuitionism, Toronto, published 2004, page 198:

(geometry, rare) A polygon with a thousand vertices and a thousand edges.


hectogon

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(geometry) A polygon having a hundred sides.


heptadecagon

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The regular 17-sided polygon (heptadecagon) can be constructed with the help of a compass and a ruler.

2001, Kunihiko Kasahara, Amazing Origami, New York, N.Y.: Sterling Publishing, →ISBN:

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


icosagon

From Ancient Greek εἰκοσάγωνος (eikoságōnos, “having twenty sides”), from εἴκοσι (eíkosi, “twenty”) + γωνία (gōnía, “angle”). Equivalent to icosa- + -gon.

uder

1993 The upper half of a regular icosagon frame is folded. - author? - Space Structures 4

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


myriagon

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For it differs in no way from the representation I should form if I were thinking of a myriagon, or any figure with very many sides.

1998, Réné Descartes, translated by Desmond M. Clarke, Meditations, Penguin, published 2003, page 58:


pentadecagon

/ˌpɛntəˈdɛkəɡən/

In ⊙ O, draw chord AB equal to r. Draw chord AC equal to Vt (which is the side of a regular decagon). CB is now one side of the regular pentadecagon.

2003, Steven Atiyah, Essentials of Geometry, Trafford, published 2003, page 357:

(geometry) A polygon with fifteen sides.


biconical

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consisting of two cones placed together apex to apex


multidimensional

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(mathematics) Having more than two dimensions.

Having multiple dimensions (aspects).
Having more than two dimensions.


cline

Let C₁ and C₂ be two nonintersecting clines. Prove that there is a unique pair of points that are simultaneously symmetric to both C₁ and C₂.

2001, Michael Henle, Modern Geometries: Non-Euclidean, Projective, and Discrete, page 77:

To visualize Möbius transformations, it is helpful to focus on fixed points and, in the case of two fixed points, on two families of clines with respect to these points.

2009, Michael P. Hitchman, Geometry with an Introduction to Cosmic Topology, page 64:

2011, Dominique Michelucci, What is a Line?, Pascal Schreck, Julien Narboux, Jürgen Richter-Gebert (editors), Automated Deduction in Geometry, 8th International Workshop, ADG 2010, Revised Selected Papers, LNAI 6877, page 139,
Let Ω be a fixed, arbitrary, point. Then circles (in the classical sense) through Ω can be considered as lines. For convenience, such circles are called clines in this section. Two distinct clines cut in one point (ignoring Ω and the two cyclic points); it can happen that Ω is a double intersection point; in this case, one may say that the two clines are parallel, and that they meet at a point at infinity, which is Ω.

(geometry, inversive geometry) A generalized circle.


oriented

en-adj

oriented (comparative more oriented, superlative most oriented)

more oriented (comparative)
most oriented (superlative)
orientated (alternative)

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(geometry, topology) In any of various technical senses, admitting or being equipped with a notion of handedness (i.e. of distinguishing clockwise and anticlockwise). See Orientability on Wikipedia.Wikipedia


pointlessness

en-noun

pointlessness (countable and uncountable, plural pointlessnesses)

(topology, geometry, uncountable) The quality of not mentioning points.


projective

en-adj

projective (comparative more projective, superlative most projective)

more projective (comparative)
most projective (superlative)

Formed by the suffixation of prōiect- (the perfect passive participial stem of the Classical Latin prōiciō, whence the English verb project) with the English -ive, forming project + -ive; however, compare the post-Classical Latin prōiectīvus (“relating to purging”).

cog

Hence the non-Euclidean angle is measured by one-half the logarithm of the cross-ratio of four rays. Although the Euclidean point of view has been adopted for simplicity, the final result, depending as it does only on the cross-ratio, is projective; it is therefore independent of the particular assumptions that the rays α and β are perpendicular and that the initial line bisects the angle between them.

1912 November 18, Edwin B. Wilson, Gillbert B. Lewis, “The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics”, in Proceedings of the American Academy of Arts and Sciences, volume 45, number 11, page 503:

(geometry) Of or related to projective geometry:

(now usually in set phrases, of a property of a geometric object, figure, etc.) Invariant under projective transformations.

now usually in set phrases; figure; now usually in set phrases; figure

(of a geometric object, figure, etc.) Defined in or inhabiting a projective space.


golden ratio

(geometry) The irrational number (approximately 1.618), usually denoted by the Greek letter φ (phi), which is equal to the sum of its own reciprocal and 1, or, equivalently, is the square root of the sum of itself and 1.

黄金比

おうごんひ ōgon hi


Pythagorean theorem

the Pythagorean theorem (canonical)
Pythagoras' theorem (alternative)
theorem of Pythagoras (alternative)

Named after Pythagoras (from Ancient Greek Πυθαγόρας (Puthagóras)), the Greek mathematician and philosopher who by tradition is credited with the theorem’s discovery and proof.

The Pythagorean theorem only applies to right triangles.

(geometry) A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.


adjoint

Adjoint representation
Adjoint representation of a Lie algebra
adjoint

/ˈæd͡ʒ.ɔɪnt/

From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.
In the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.

The sets A + A₀, B + B₀, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B₀ consists of p points, and lies on i + j adjoint φ-curves of f = 0.

1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103:

As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r#95;i-1 at each point where f has the multiplicity r#95;i. A first polar #92;sum#95;iy#95;i#92;left(#92;partialf#47;#92;partialx#95;i#92;right)#61;0 is an example of an adjoint curve.

1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205:

This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.

2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216:

(geometry, of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.


adjoint

/ˈæd͡ʒ.ɔɪnt/

(geometry, algebraic geometry) A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.


polarity

en-noun

polarity (countable and uncountable, plural polarities)

(projective geometry) A duality that is an involution, i.e. has order two. ᵂᵖ

trilinear polarity
trilinear polarity#English

(geometry) Ellipsis of trilinear polarity.


one-dimensional

en-adj

one-dimensional (comparative more one-dimensional, superlative most one-dimensional)

more one-dimensional (comparative)
most one-dimensional (superlative)
onedimensional (alternative)

(figuratively) Lacking personal depth and substance; conceited, vain, shallow, superficial.


bounding

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(geometry) Containing all points of a given set within it.


foliate

foliate (comparative more foliate, superlative most foliate)

more foliate (comparative)
most foliate (superlative)

Learned borrowing from Latin foliātus (“having leaves, leafy, leaved”) (see -ate (adjective-forming suffix)), a participial adjective derived from folium (“leaf; (Late Latin) leaf or sheet of paper”) + -ātus (participial adjective-forming suffix) (ultimately from Proto-Indo-European *bʰleh₃- (“blossom, flower”) or *dʰelh₁- (“to be green”)).

der

Shaped like or otherwise resembling a leaf; leaflike.

(geometry) Of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop.

lehti-

of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop


foliate

From a substantivation of the above adjective. Equivalent to folia + -ate (noun-forming suffix).


compass error

(geometry, geomagnetism) The combination of variation and deviation which is the horizontal angle between the direction indicated by a magnetic compass and true north.


exterior angle

(geometry) An angle formed between one side of a polygon and an extension of an adjacent side.

vnější úhel

an angle formed between one side of a polygon and an extension of an adjacent side


boxcar function

en-noun

boxcar function (plural boxcar functions)

Due to the graph resembling a rectangular boxcar on a railway line.

(calculus, geometry) Any function whose value is zero except for a finite part of its argument for which it has a constant non-zero value.


elliptic

From Ancient Greek ἐλλειπτικός (elleiptikós), from ἐλλείπω (elleípō, “I leave out, omit”). By surface analysis, ellipse + -tic.

Novv ſince the Planets move in Elliptick Orbits, in one of vvhoſe foci the Sun is, and by a Radius from the Sun deſcribe equal Area's in equal Times, vvhich no other Lavv of a Circulating Fluid, but the Harmonical Circulation can Account for, vve muſt find out a Lavv for the Paracentrical Motion, that may make the Orbits Elliptick.

1705, George Cheyne, “Of the Physical Laws, and the Uniform Appearances of Nature. Law III.”, in Philosophical Principles of Natural Religion: […], London: […] George Strahan […], →OCLC, § XXIV, page 39:

In this chapter, the history of solving elliptic problems by direct marching methods is reviewed.

1995, Patrick J. Roache, Elliptic Marching Methods and Domain Decomposition, page 1:

(geometry) Of or pertaining to an ellipse.

эліптычны

relating to an ellipse or its mathematical definition


rectification

rectification (countable and uncountable, plural rectifications)

/ˌɹɛktɪfɪˈkeɪʃən/

From Middle English rectificacioun, from Old French rectificacion, from Late Latin rectificatio.

(geometry) The determination of a straight line whose length is equal to a portion of a curve.

(geometry) The truncation of a polyhedron by replacing each vertex with a face that passes though the midpoint of each edge connected to the vertex; an analogous procedure on a polytope of dimension higher than 3.


cubical

en-adj

cubical (comparative more cubical, superlative most cubical)

more cubical (comparative)
most cubical (superlative)

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squared

The children were taught to plot graphs on squared paper.

(geometry) Covered with a grid of squares.


escribe

en-verb

escribe (third-person singular simple present escribes, present participle escribing, simple past and past participle escribed)

escribes (present singular third-person)
escribing (participle present)
escribed (participle past)
escribed (past)

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From Latin e (“out, out of”) + scribere (“to write”).

(transitive, geometry) To draw outside of; designating a circle that touches one of the sides of a given triangle, and also the extensions of the other two sides.


segment

From Latin segmentum (“a piece cut off, a strip, segment of the earth, a strip of tinsel”), from secāre (“to cut”).

jaoke

botany: portion of an organ derived from a single cell within the primordium

(geometry) The part of a circle between its circumference and a chord (usually other than the diameter).

(geometry) The part of a sphere cut off by a plane.

сегмент

geometry: part of a sphere cut off by a plane


squarely

en-adv

squarely (comparative more squarely, superlative most squarely)

more squarely (comparative)
most squarely (superlative)

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From square + -ly. First use appears c. 1557 in the writings of Robert Recorde.

(geometry) In the shape of a square; at right angles.


double point

(geometry) A point on a curve at which there are two tangents (because it touches itself, or has a cusp).


coaxial

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ellipsoid

Polarizability can be imagined as a three-dimensional ellipsoid centred on the centre of the molecule, as shown in Figure 10.4.

2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133:

Because only ellipsoids of rotation have been adopted in practical geodesy and surveying and triaxial ellipsoids have been limited to theoretical studies, we will use the term ellipsoid for brevity to mean ellipsoid of rotation.

2004, Alfred Leick, GPS Satellite Surveying, 3rd edition, page 367:

As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the earth.

2010, Jan Van Sickle, Basic GIS Coordinates, 2nd edition, page 73:

Cartesian coordinates
Cartesian coordinates

(mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 1.

elipsoide

surface all of whose cross sections are elliptic or circular


golden section

(geometry) the division of a whole into two parts such that the ratio of the smaller part to the larger is equal to the ratio of the larger part to the whole.


radio-

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radiosymmetrical


homology

en-noun

homology (countable and uncountable, plural homologies)

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Henri Poincaré
Homology
MathWorld
singular homology

From Latin homologia, from Ancient Greek ὁμολογία (homología, “agreement, assent”); compare French homologie. By surface analysis, homo- + -logy.
In topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.

homologia

biology, psychology: relationship of having a common evolutionary or developmental origin

1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,
Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology].

1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11,
Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology.

The relationship of being homologous; a homologous relationship.

(geometry, projective geometry) specifically, such relationship in the context of the geometry of perspective.

If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.

perspective projection
perspective projection

(geometry, projective geometry) An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.

samankaltaisuus

geometry: automorphism representing a perspective projection


incidence

en-noun

incidence (countable and uncountable, plural incidences)

From Middle French incidence, from Medieval Latin incidentia (“a falling upon”), from Latin incidens, present participle of incidere (“to fall upon”), from in (“on”) + cadere (“to fall”).

der

(geometry) The falling of a point on a line, or a line on a plane.

kuuluminen

geometry: falling of a point on a line, or a line on a plane


line segment

(geometry) A part of a straight line bounded by two points.


subnormal

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w:Webster's Dictionary#Webster's New International Dictionary 1909

(geometry) That part of the axis of a curved line which is intercepted between the ordinate and the normal.


plane angle

en-noun

plane angle (countable and uncountable, plural plane angles)

(geometry) An angle formed by two intersecting straight lines.

rovinný úhel

(geometry) An angle formed by two intersecting planes, measured by the angle between two intersecting straight lines that are in respective planes and perpendicular to the intersection of the planes.


cathetus

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From Latin cathetus, from Ancient Greek κάθετος (káthetos, “perpendicular”).

uder

(geometry) A line perpendicular to a surface (or line); in particular, either of the sides of a right triangle other than its hypotenuse.


incenter

incenters (plural)
incentre (alternative)

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(US, geometry) The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.


spheroidal

en-adj

spheroidal (comparative more spheroidal, superlative most spheroidal)

more spheroidal (comparative)
most spheroidal (superlative)

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The buccal mass in milacids is spheroidal, and contains an oxygnathic jaw.

2004, G. M. Barker, Natural Enemies of Terrestrial Molluscs, page 299:


confluent

confluent (comparative more confluent, superlative most confluent)

more confluent (comparative)
most confluent (superlative)

(geometry, of a triangle) Exactly the same size as another triangle.


coplanar

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(geometry, of at least two things, usually lines or plane figures) Within the same plane.


convex hull

1994, David Eppstein, Chapter 10: Average Case Analysis of Dynamic Geometric Optimization, Association of Computing Machinery, Society for Industrial and Applied Mathematics, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, page 83,
This problem can be solved in time O(nᶜ) by combining a weight-balanced tree of the convex hull vertices with a farthest neighbor data structure of Agarwal and Matoušek [2].

Thus, the polyhedron and the convex hull of the set of its vertices coincide, which was to be proved.
Since the convex hull of a set M is determined uniquely from M, Theorem 1 implies that a bounded solid polyhedron and its surface, i.e., a closed convex polyhedron, are determined uniquely from its vertices.

2005, A.D. Alexandrov, Convex Polyhedra, page 23:

The convex hull of a compact subset of an infinite dimensional topological vector space need not be a compact set.

2007, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, page 185:

(mathematics) The smallest convex set of points in which a given set of points is contained.

convex envelope

smallest convex set of points containing a given set


supplementary angle

en-noun

supplementary angle (plural supplementary angles)

Angle A is 40°, and its supplementary angle, B, is 140°.

(geometry) An angle that, when added to another referenced angle, produces an angle of 180 degrees.


oblique angle

oblique angles (plural)
obliquangle (alternative obsolete)

(geometry) Any angle that is not a right angle or multiple of right angles.

vino kulma

any angle that is not a right angle or multiple of right angles


right-angled

(not comparable, geometry) Having a right angle.


icosihenagon

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From Ancient Greek εἰκοσιέν (eikosién, “twenty-one”) + -gon.

uder

(geometry) A polygon with twenty-one edges and twenty-one angles.


Euclidian space

en-noun

Euclidian space (countable and uncountable, plural Euclidian spaces)

(mathematics, geometry) A space where the principles of Euclidean geometry apply.


centroid

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From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

barycentre

centre of gravity of a uniform, rigid object

barycentre

centre of gravity of a set of points of equal mass

The center of gravity of any body or geometrical magnitude is by definition the same as the centroid of a certain system of parallel forces. It will be convenient, therefore, to use the word centroid in most cases instead of center of gravity.[…]The centroid of any area may be found by the following method: Divide the area into parts such that the area and centroid of each part are known. Take the centroids of the partial areas as the points of application of forces proportional respectively to those areas. The centroid of this system of forces is the centroid of the total area, and may be found by the method of Art. 172.

1892, Leander Miller Hoskins, The Elements of Graphic Statics, MacMillan and Co., pages 151–152:

For example, if a postal code area (PCA) has 1000 distinct residences, we might suppose all 1000 residences are at the centroid of the PCA. Centroids are commonly used, for example, with geographic information systems and CD-ROM phone books (Francis, Lowe, Rushton and Rayco 1999).

2004, Richard L. Francis, Timothy J. Lowe, Arie Tamir, “7: Demand Point Aggregation for Local Models”, in Zvi Drezner, Horst W. Hamacher, editors, Facility Location: Applications and Theory, Springer-Verlag, page 207:

operatorname Centroid(𝒳)=(∫xg(x)dx)/(∫g(x)dx)      (6)
where the integrals are taken over the whole space ℝⁿ, and g is the characteristic function of the subset, which is 1 inside 𝒳 and 0 outside it [27].

2020, Cheng Zhang, Qiuchi Li, Lingyu Hua, Dawei Song, Assessing the Memory Ability of Recurrent Neural Networks, Giuseppe De Giacomo, et al. (editors), ECAI 2020: 24th European Conference on Artificial Intelligence, IOS Press, page 1660, In ℝⁿ, a centroid is the mean position of all the points in all of the coordinate directions. The centroid of a subset 𝒳 of ℝⁿ is computed as follows

(geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.

形心

mean position of points in a geometrical figure — see also center of gravity, barycenter

(geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.


holonomy

holonomy (countable and uncountable, plural holonomies)

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differential geometry
differential geometry

(differential geometry) Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.


axis of symmetry

axis of symmetry (plural axes of symmetry)

(geometry) Any of one or more lines about which a geometric figure is symmetric

о́с на симе́трия

a line about which a geometric figure is symmetric


square pyramid

Great Pyramid of Giza
Great Pyramid of Giza

(geometry) A three-dimensional geometric figure with a square base and four triangular sides that connect at one point. An example is the Great Pyramid of Giza.


triangularly

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central angle

(geometry) An angle positioned with its vertex at the center of a circle.

keskuskulma

an angle positioned with its vertex at the center of a circle


parallelepipedal

(geometry) Having the form of a parallelepiped


hyperspatial

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Of or pertaining to multi-dimensional geometry.


fixed set

(mathematics) A set which is unchanged by a function or other mapping. Formally: a set, S, is a fixed set of a function, f, if and only if for all x in S, f(x)=x.


truncated icosahedron

truncated icosahedron (plural truncated icosahedra or truncated icosahedrons)

truncated icosahedra (plural)
truncated icosahedrons (plural)

From truncated + icosahedron.
Truncatedicosahedron.gif|regular truncated icosahedron
Buckminsterfullerene animated.gif|C₆₀: buckminsterfullerene
Comparison of truncated icosahedron and soccer ball.png|A soccer ball with a regular truncated icosahedron

A truncated icosahedron may be formed by truncating the vertices of an icosahedron. Each vertex of the icosahedron is replaced by a pentagonal face and each triangular face of the icosahedron is replaced by a hexagonal face, which is inscribed inside the triangular face of the original icosahedron. The entire resulting truncated icosahedron is thus fittingly inscribed inside the original icosahedron.

This is the truncated icosahedron. Where the five triangles meet to form a vertex is now a pentagon, and a hexagon now replaces each triangular face. Therefore, the truncated icosahedron is composed of twelve pentagons and twenty hexagons.

1989, Tony Rothman, Science a la Mode: Physical Fashions and Fictions, page 64:

In addition to the 20 lithium atoms in layer b, additional lithium atoms (layer e) are located above the twelve pentagonal faces of the peripheral truncated icosahedra which, because of the way that the truncated icosahedra are linked, simultaneously cap the pentagonal faces of two adjacent truncated icosahedra sharing an edge (sharing method 1 above).

1993, R. Bruce King, Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry, page 183:

Fullerenes are truncated icosahedrons with 90 edges of equal length, 60 vertices, 20 hexagonal faces, and 12 pentagonal faces that form a closed shell.

2001, Edward A. Rietman, Molecular Engineering of Nanosystems, page 130:

2008, Jill Vincent, Andy Edwards, David Tynan, Gloria Stillman (editors), MathsWorld Year Eight for Queensland, Teacher Edition, page 308,
Do you know which sport is played with a truncated icosahedron?

(geometry) A polyhedron that has thirty-two faces (12 regular pentagons and 20 regular hexagons) and 60 vertices and 90 edges, and is one of the Archimedean solids.


nonagonal

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surface area

surface area (countable and uncountable, plural surface areas)

(geometry) The total area on the surface of an object.


trisection

trisection (countable and uncountable, plural trisections)

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A traditional (but impossible) mathematical problem was to achieve trisection using a straight edge and compass.

(geometry) The division of an angle into three equal parts.


tiling

tiling (countable and uncountable, plural tilings)

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(geometry) A tessellation; the covering of a plane with shapes, without overlaps or gaps.


slab

From Middle English sclabbe, slabbe, of uncertain origin; possibly from *slap, related to dialectal slappel (“portion, piece”), along with slape (“slippery”), sleip (“smooth piece of timber”), borrowed through Old Norse sleipr from Proto-Germanic *slaipaz, from Proto-Indo-European *(s)leyb-. See also Norwegian sleip (“slippery”) and Icelandic sleipur.

(geometry) A region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space, or between two hyperplanes in higher dimensions.


evolute

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centres of curvature
centre of curvature

(geometry) A curve comprising the centres of curvature of another curve.

evoluta

a curve comprising the centres of curvature of another curve


verging

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rectilinear

en-adj

rectilinear (comparative more rectilinear, superlative most rectilinear)

more rectilinear (comparative)
most rectilinear (superlative)

/ˌɹɛktɪˈlɪniɚ/

/ˌɹɛktɪˈlɪnɪə/

From post-Classical Latin; either from rectilīneāris or from rectilīneus (whence rectiline) + -ar, in both cases ultimately deriving from rectus (“straight”) + līnea (“line”).

(geometry, art) Formed from straight lines.


(geometry) Synonym of pentacontagon: A 50-sided polygon.


rigidification

/ɹɪˌd͡ʒɪdɪfɪˈkeɪʃən/

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(geometry) A form of isomorphism applied between line bundles.


differential geometry

en-noun

differential geometry (usually uncountable, plural differential geometries)

1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,
[…] projective differential geometries of the American and Italian schools do not seem to have attracted physicists.

1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,
The general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces.

Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.

1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v:

In this sense, C#123;k#95;0#125; is the natural hypothesis of differentiability in the particular question of differential geometry.

2012, Heinrich W. Guggenheimer, Differential Geometry, page 145:

mathematical analysis
mathematical analysis

differentiable manifold
differentiable manifold

(geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.


homographic

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From homo- + -graphic; alternatively, homograph + -ic.


quadrate

quadrates (plural)
quadrat (alternative obsolete)

From Middle English quadrat, quadrate, from Latin quadrātum. Doublet of quadrat; compare also quadrant (“square or quadrangle”).

At which command, the powers militant
That stood for heav'n, in mighty quadrate joyn'd.

1667, John Milton, “Book V”, 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, lines 61-62:

(geometry) A plane surface with four equal sides and four right angles; a square; hence, figuratively, anything having the outline of a square.


spherule

spherules (plural)
sphærula (alternative obsolete)
sphærule (alternative obsolete)
sphaerula (alternative uncommon)
sphaerule (alternative uncommon)
spherula (alternative)

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From Latin sphērula, sphaerula, from sphēra, sphaera (“sphere”) + -ula (diminutive suffix).


semimajor axis

semimajor axes (plural)
semi-major axis (alternative)

(geometry) Half of the major axis of a circle or ellipse.

半長軸 /半长轴

half of the major axis of a circle or ellipse

(geometry) Half of the distances between the two branches of a hyperbola.


major axis

(geometry) The longest diameter of an ellipse, running through the center and foci, with its ends being the widest points of the shape.

halkaisija

diameter of a circle — see also diameter


pentahedron

pentahedron (plural pentahedrons or pentahedra)

pentahedrons (plural)
pentahedra (plural)

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Their tent was too small for them to stand, a long but low pentahedron, in shape like the triangular glass prism Saeed used to have as a child, with which he would refract sunlight into little rainbows.

2017, Mohsin Hamid, Exit West, Hamish Hamilton, page 106:

(geometry) A polyhedron with five faces.


subconical

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(geometry, mycology) Shaped somewhat like a cone.


apolar

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(geometry) Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.


rhombitruncated icosidodecahedron

rhombitruncated icosidodecahedron (plural rhombitruncated icosidodecahedrons)

(geometry) An Archimedean solid composed of 122 faces, 120 vertices, and 240 edges.


stellate

en-verb

stellate (third-person singular simple present stellates, present participle stellating, simple past and past participle stellated)

stellates (present singular third-person)
stellating (participle present)
stellated (participle past)
stellated (past)

From stell(a) + -ate (verb-forming suffix).

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(geometry) To extend the edges or planes of a polyhedron to form a new shape.


sail curve

(geometry) A catenary-generated curve in the form of a cross-section of a sail filled by wind.


Heron's formula

The formula A=√, where a, b, and c are the sidelengths of a triangle, s is its semiperimeter, and A is its area.


oblatum

From Late Latin oblātus (oblatus), from Latin ob (“in front of, before”) + lātus (“broad, wide”), (modelled after and contrasting with prolatus (“extended, lengthened”)).

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(geometry) An oblate spheroid; a figure described by the revolution of an ellipse about its minor axis.


half-line

(geometry) ray; a line extending indefinitely in one direction from a point.


analytic geometry

Having thus noted the distinction between Analytic Geometry and Geometry, let us note in what way it differs from Algebra.

1889, Arthur Sherburne Hardy, Elements of Analytic Geometry, Ginn, published 1891, page 12:

1921, Claude Irwin Palmer, William Charles Krathwohl, Analytic Geometry, McGraw-Hill, page 261,
In plane analytic geometry, all the points and lines are confined to one plane.

2018, Peter Kuhfittig, Technical Calculus with Analytic Geometry, 5th Edition, Cengage Learning (BROOKS/COLE), page 1,
Analytic geometry may be defined as the study of classical geometry by means of algebra.

(geometry) The subbranch of geometry that investigates geometrical figures via the mathematical properties of their representations in a coordinate system.


circular sector

en-noun

circular sector (plural circular sectors)

circular sectors (plural)
circle sector (alternative)

(geometry) A portion of a circle enclosed by two radii and an arc.


dirigent

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From Latin dīrigēns, present participle of dīrigō.

The straight line in which the vertical polar plane cuts the plane of the circle of contact is called the dirigent. As there are in general two circles of contact, there are two dirigents, and they are parallel to the diretrices.

1877, James Booth, A Treatise on Some New Geometrical Methods, page 348:

In this case, to which Sphero-Cartesians, and all other sphero-quadrics, whose dirigents are small circles, are analogous in Spherics, the dirigent conic F must also have double contact with S.

1891, Proceedings of the London Mathematical Society, volume 21, page 308:

(dated, geometry) The line of motion of a describent line or surface that in so moving defines a plane or solid figure; a directrix.


bicapped

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(geometry, of a prism) Having a cap (in the shape of a pyramid) at each end


directrix

directrix (plural directrixes or directrices)

directrixes (plural)
directrices (plural)

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Learned borrowing from Latin dīrectrīx. By surface analysis, direct + -trix.

(geometry) A line used to define a curve or surface; especially a line, the distance from which a point on a conic has a constant ratio to that from the focus.

richtlijn

a line used to define a curve or surface


monogon

A geodesic with multiple points contains at least one simple monogon.

1955, Herbert Busemann, The Geometry of Geodesics, page 295:

There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.

1981, Harold Abelson, Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262:

2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, →ISBN, page 409,
We explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?

(geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#43;2 edges, and 4s#43;2 faces. Of these faces, 4s#43;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.

1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:

2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158,
There is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).

An end-compressing monogon for F is a monogon properly embedded in the complimentary^([sic]) region C which is not homotopic (rel. boundary) into #92;partialC.

a. 2006, Thilo Kuessner, “A survey on simplicial volume and invariants of foliations and laminations”, in Paweł Walczak et al., editors, Foliations 2005, →ISBN, page 295:

(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.


digon

From di- (prefix meaning ‘two’) + -gon (suffix forming the names of plane figures containing a given number of angles).

confix

monogon · digon · trigon · tetragon · pentagon · hexagon · heptagon · octagon · nonagon · decagon · undecagon · dodecagon · see also Category:English terms suffixed with -gon

They [the students] also came upon new and unusual mathematical figures: the digon, a two-sided polygon on a spherical space, and the apeirogon, an open polygon with infinitely many sides […]. All these discoveries brought up even more questions. Is a circle a polygon? What makes an octagon an octagon – its eight vertices, its eight sides, or both? Can a polygon cross itself? Does a polygon need to be closed?

2013, Brent Davis, Moshe Renert, chapter 6, in The Math Teachers Know: Profound Understanding of Emergent Mathematics, New York, N.Y., Abingdon, Oxfordshire: Routledge, →ISBN, page 102:

(geometry) A polygon having two edges and two vertices.


tridecagon

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(geometry) A polygon having thirteen sides and thirteen angles.


tetradecagon

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(geometry) A polygon having fourteen sides and fourteen angles.


apeirogon

/əˈpiːɹɵɡɑn/

/əˈpeɪ̯ɹɵɡɑn/

/əˈpɪəɹəɡən/

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.

1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:

In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.

1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:

[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.

2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:

There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.

2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:

(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;

A type of generalised polygon with a countably infinite number of sides and vertices;
(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.


zerogon

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(geometry) A circle visualized as a polygon having no edges or vertices.


achiral

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(geometry, physical chemistry) superimposable on its mirror image; amphichiral


amphichiral

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(geometry, physical chemistry) superimposable on its mirror image; achiral


cylindrically

en-adv

cylindrically (comparative more cylindrically, superlative most cylindrically)

more cylindrically (comparative)
most cylindrically (superlative)

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circumcenter

circumcenters (plural)
circumcentre (alternative)

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(geometry) The center of a circumcircle (the circle that passes through every vertex of a given triangle or other cyclic polygon).


mediatrix

en-noun

mediatrix (plural mediatrices or mediatrixes)

mediatrices (plural)
mediatrixes (plural)

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Learned borrowing from Late Latin mediātrīx. By surface analysis, mediator + -trix.

lbor

[…] the intersection of the normal at M to the parabola with the mediatrix of the line […]

2000, Jean H. Gallier, Curves and surfaces in geometric modeling, page 105:

(geometry, rare) A bisector, the line that is perpendicular to a line segment and intersects the line segment at its midpoint.


nonchiral

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(geometry, physical chemistry) Not chiral.


stellated

en-adj

stellated (comparative more stellated, superlative most stellated)

more stellated (comparative)
most stellated (superlative)

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(geometry) Of a polyhedron, having its edges or planes extended to form a new shape.


isosceles trapezoid

en-noun

isosceles trapezoid (plural isosceles trapezoids)

A quadrilateral with two parallel sides and a separate pair of congruent sides which are not parallel.

等腰梯形

quadrilateral with two parallel sides and separate pair of congruent sides that are not parallel


halfspace

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(geometry) Either of the two parts of a three-dimensional object cut by a two-dimensional plane


superposability

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trochoid

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From Ancient Greek τροχοειδής (trokhoeidḗs), from τροχός (trokhós, “wheel”) + εἶδος (eîdos, “form, image”).

(geometry) The curve traced by a point on a circle as it rolls along a straight line


stereotomy

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From French stéréotomie, equivalent to stereo- + -tomy.

Here your countenance brightened up, and, perceiving your lips move, I could not doubt that you murmured the word ‘stereotomy’, a term very affectedly applied to this species of pavement.

1841, Edgar Allan Poe, The Murders in the Rue Morgue:

(geometry, masonry) The cutting or dissection of solids.


osculatory

en-adj

osculatory (comparative more osculatory, superlative most osculatory)

more osculatory (comparative)
most osculatory (superlative)

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A circle may be osculatory with a curve, at a given point.

(geometry) Relating to, or having the properties of, an osculatrix; capable of osculation.


traverse

From Middle English traversen, from Old French traverser, from Latin trans (“across”) + versus (“turned”), perfect passive participle of Latin vertere (“to turn”).

(geometry) A line lying across a figure or other lines; a transversal.


sphericity

en-noun

sphericity (countable and uncountable, plural sphericities)

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From spheric + -ity. In the geometrical sense, defined by the geologist Hakon Wadell in 1935.

(geometry, countable) The ratio of the surface area of a given particle to the surface area of a sphere with the same volume.

pallonmuotoisuus

ratio of particle surface area to sphere surface area


osculating circle

osculating circle (plural osculating circles)

(geometry, for any point on a curve) The circle that has the same tangent, and the same curvature at the point on the curve.


birectangular

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Unlike a normal triangle, a spherical triangle can be birectangular because the sum of its angles is greater than 180 degrees.


dihedron

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(geometry) A polyhedron having two faces


flexagon

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(geometry) A flat model made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.

флексаго́н

a flat model made from folded strips of paper


circular segment

circular segment (plural circular segments)

(geometry) A region of a circle bounded by an arc and the chord connecting the endpoints of the arc.


orthant

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Consider preferences defined over the nonnegative orthant by (x#95;1,x#95;2)#92;succ(y#95;1,y#95;2) if x#95;1#43;x#95;2lt;y#95;1#43;y#95;2 […]

1992, Hal R. Varian, Microeconomic Analysis, 3rd edition, Norton, page 114:

(geometry) A n-dimensional generalization of the quadrant (in two-dimensional Cartesian space) and octant (in three-dimensional space).


epitrochoid

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A geometric curve traced by a fixed point on one circle which rotates around the perimeter of another circle. Examples include the shape of the Wankel engine


hypotrochoid

(geometry) A geometric curve traced by a fixed point on the radius line outside one circle which rotates inside the perimeter of another circle.


dodecadodecahedron

dodecadodecahedron (plural dodecadodecahedra or dodecadodecahedrons)

dodecadodecahedra (plural)
dodecadodecahedrons (plural)

/ˌdəʊdɛkəˌdəʊdɛkəˈhiːdɹən/

/ˌdəʊdɪkəˌdəʊdɪkəˈhiːdɹən/

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(geometry) A nonconvex polyhedron with twenty-four faces, thirty vertices, and sixty edges.


hyperplane

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We now have good reason to question the pursuits of the vaunted innovators with whom Liu consorted in California – the blissed-out cultists at Google, whose only worry is over “the wrong kind of sparkling water in the microkitchens”, or the manic experts who specialise in “envisioning hyperplanes in n-dimensional space”.

2020 April 7, Peter Conrad, “Abolish Silicon Valley by Wendy Liu review – rebooting our reality”, in The Guardian:

(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)

nadrovina

an n-dimensional generalization of a plane


conus

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generant

en-adj

generant (comparative more generant, superlative most generant)

more generant (comparative)
most generant (superlative)

/ˈd͡ʒɛnəɹənt/

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generant

/ˈd͡ʒɛnəɹənt/


disphenoid

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From di- (“twice, double”) + sphenoid (“wedge-shaped crystal or bone of the skull”).

prefix

The mineral chalcopyrite commonly crystallizes in disphenoids that are very difficult to distinguish from tetrahedrons.

1949, Edward Salisbury Dana, Minerals and How to Study Them, page 32:

1973, H. S. M. Coxeter, 3rd Edition, unnumbered page,
To make a model of a disphenoid, cut out an acute angled triangle and fold it along the joins of the mid-points of the sides. The disphenoid is said to be rhombic or tetragonal according as the triangle is isosceles or scalene.

If you rotate the [tetragonal] disphenoid 90° around its 2-fold axis and then perform the operation of inversion through the center-point of the object, it will occupy its original position again.

1977, Elizabeth A. Wood, Crystals and Light: An Introduction to Optical Crystallography, Revised edition, page 8:

In addition it should be remarked that there are two types of disphenoids, with different symmetries: the tetragonal disphenoid (having isosceles facets) and the rhombic one.

1993, Horst Martini, “A Hierarchical Classification of Euclidean Polytopes with Regularity Properties”, in Tibor Bisztriczky, Peter McMullen, Rolf Schneider, Asia Ivic Weiss, editors, Polytopes: Abstract, Convex and Computational, Proceedings of the NATO Advanced Study Institute, page 83:

(geometry) A non-regular tetrahedron whose four faces are congruent acute-angled triangles.

bisphenoid

non-regular tetrahedron with congruent faces


sinistrorse

en-adj

sinistrorse (comparative more sinistrorse, superlative most sinistrorse)

more sinistrorse (comparative)
most sinistrorse (superlative)

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concyclic

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(geometry, of a set of points) Lying on a common circle.


barycenter

barycenters (plural)
barycentre (alternative)

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(geometry) The centroid, the geometric center of a plane figure


isosurface

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an isosurface representing a concentration of 10 grams per cubic meter

(computer graphics, geometry) A surface that represents points of a constant value within a volume of space


semimajor

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a semimajor radius

(geometry) Of or pertaining to the semimajor axis, the long axis of an ellipse


cuboidal

cuboidal (comparative more cuboidal, superlative most cuboidal)

more cuboidal (comparative)
most cuboidal (superlative)

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A cuboidal block was formed.

(geometry) Of, pertaining to, or having the shape of a cuboid


coplanarity

en-noun

coplanarity (countable and uncountable, plural coplanarities)

coplanarities (plural)
co-planarity (alternative)

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(geometry, of at least two things, usually lines) The state or characteristic of being within the same plane.


monogonal

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(geometry) Of or pertaining to a monogon.


monogonal

(geometry, of a line) That passes through exactly one vertex (of a polygon or polyhedron).


horocycle

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(geometry) A curve in hyperbolic geometry whose normals all converge asymptotically.


developable

en-adj

developable (comparative more developable, superlative most developable)

more developable (comparative)
most developable (superlative)

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(geometry, of a surface) Described by a moving right line, and such that consecutive positions of the generator intersect each other, allowing the surface to be developed into a plane.


quadratically

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In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation.

2015, Anja Marunović, Tomislav Prokopec, “Topological inflation with graceful exit”, in arXiv:


semiregular

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It will be seen below that this semiregular polyhedron is of importance in its relationship to periodic minimal surfaces serving as a conceptual reference.

1993, H. Terrones, A. L. MacKay, “The Geometry of Hypothetical Curved Graphite Structures”, in H. W. Kroto, J.E. Fischer, Deann Cox, editors, The Fullerenes, page 115:

In a semiregular tessellation, there is an isometry of the plane carrying any vertex to any other vertex.

1998, David A. Singer, Geometry: Plane and Fancy, page 35:

While one of the semiregular polyhedra was mentioned by Plato, their first serious study is attributed to Archimedes.

2003, Saul Stahl, Geometry from Euclid to Knots, published 2010, page 272:

One that we will consider here is the semiregular tessellation—a tessellation of two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point. The tessellation at the left in Figure 9.38 is a semiregular tessellation because the two figures are a square and a regular octagon. The tessellation at the right in Figure 9.38 is not a semiregular tessellation because the two figures are a square and a nonregular octagon.[…]There are only eight possible semiregular tessellations.

2011, Tom Bassarear, Mathematics for Elementary School Teachers, page 583:

(geometry, of a polyhedron or tessellation of the plane) Uniform (isogonal and isotoxal) with regular faces of two or more types, such that each vertex is surrounded by the same polygons in the same order.


spherical angle

en-noun

spherical angle (plural spherical angles)

(geometry) A particular dihedral angle, the angle between two intersecting arcs on a sphere, measured by the angle between the planes containing the arcs.


hexecontahedron

hexecontahedra (plural)
hexacontahedron (alternative)

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From Ancient Greek ἑξήκοντα (hexḗkonta, “60”) + -hedron, from Ancient Greek ἕδρα (hédra, “geometric face”).


zonohedron

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(geometry) A special case of convex polyhedron, in which every face of the polyhedron is a polygon with point symmetry.

chamfered cube
rhombic dodecahedron
zonohedron


zonotope

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(geometry) A polytope formed by the Minkowski sum of a zonohedron's line segments in any dimension.


inscribable

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(geometry) That can be inscribed; whose vertices all lie on a sphere.


tetrahedralizable

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(geometry) That can be divided into tetrahedra.


starlike

en-adj

starlike (comparative more starlike, superlative most starlike)

more starlike (comparative)
most starlike (superlative)

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the growth theorem for holomorphic starlike mappings

(geometry) Convex; having the property that any line segment joining any mapped point to a specified point in the domain lies entirely in the domain.


antipole

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A line drawn from a point on a circle to its antipole will cross through the center.

(geometry) A position directly opposite (possibly also used figuratively).


megagon

Find the constant of proportionality for a decagon, kilogon, and megagon.

1999, Mark Dugopolski, College Algebra and Trigonometry, page 505:

There can exist a regular polygon with 1000 sides (this might be called a "regular kilogon"), 1,000,000 sides (a "regular megagon"), or 1,000,000,000 sides (a "regular gigagon").

2003, Stan Gibilisco, Geometry Demystified:

A megagon is close to the perfection of a circle — a kind of generational transmutation.

2007, Arthur Greenberg, From Alchemy to Chemistry in Picture and Story:

(geometry) A polygon with one million sides.


prototile

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(geometry) Any of the minimal set of non-congruent shapes from which a larger set of shapes, some of which may be congruent, can be produced.


lateral area

(geometry) The sum of the areas of the lateral (vertical) faces of a cylinder, cone, frustum, or the like.


hendecagonal

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(geometry) Having eleven sides and angles; similar to a hendecagon


tridecagonal

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(geometry) Having thirteen sides and angles, similar to a tridecagon.

13-kulmion muotoinen

having thirteen sides and thirteen angles


Reuleaux triangle

en-noun

Reuleaux triangle (plural Reuleaux triangles)

Named after Franz Reuleaux, 19th-century German engineer, who used Reuleaux triangles in his machine designs.

(geometry) A figure consisting of three circular arcs, each centered on the intersection of the other two.


hyperellipse

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The hyperellipse is defined by (x/a)ⁿ + (y/b)ⁿ = 1 with b ≤ a, where n is the shape parameter and a and b are the axes along the x and y axes, respectively.

2003, M. M. Yovanovich and E. E. Marotta, "Thermal Spreading and Contact Resistances", chapter 4 of Adrian Bejan and Allan D. Kraus (editors), Heat Transfer Handbook, Wiley-IEEE, page 286

(geometry) A superellipse: a curve in two dimensions of a certain type, a generalization of the ellipse.

(geometry) Specifically, a superellipse with an exponent (shape parameter) greater than that of the ellipse (two).

This algorithm extends the model of RNS by incorporating multiple hypershape (hypersphere, hyperrectangle, or hyperellipse) detector representation in the unit hypercube [0, 1]ⁿ (Balachandran et al., 2007).

2008, Dipankar Dasgupta, Luis Fernando Niño, Immunological Computation: Theory and Applications, CRC Press, →ISBN, page 97:

(geometry) A multi-dimensional manifold of a certain type, a generalization of the ellipse and ellipsoid.


blockwise

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(geometry) Allowing movement vertically or horizontally only, as if navigating the edges of a grid pattern.


tractrix

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Formed after tractor, as if from a Latin *tractrīx (from trahō (“to pull”) + -trīx).

(geometry) A curve that satisfies the following property: that segment of the tangent line that lies between the point of tangency and a fixed line has length independent of the point of tangency chosen.


ungula

Borrowed from Latin ungula (“claw, hoof”), from unguis (“nail, claw, hoof”).

(geometry) A section of a cylinder, cone, or other solid of revolution, cut off by a plane oblique to the base; so called from its resemblance to the hoof of a horse.


superficies

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Borrowing from Latin superficiēs (“top, surface”), from super- (“above, over”) + faciēs (“form, configuration, shape”). Doublet of surface.

af

(geometry) A two-dimensional magnitude that has length and breadth; especially such a surface that forms the boundary of a solid.

The Superficies was compoſed of ſeveral bits of Wood, about the bigneſs of a Dye, but ſome larger than others.

1726 October 28, [Jonathan Swift], “The Author Permitted to See the Grand Academy of Lagado. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 72:

The visible, external surface of a body.


pseudocubic

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(geometry) describing a rhombohedral structure that is almost cubic


homothecy

Let us determine the center and the ratio of this homothecy.

1950, Duke Mathematical Journal, Duke University Press, page 76:

The restriction of B to S_b is a homothecy of scale b.

1981, Kenneth Joseph Arrow, Michael D. Intriligator, Handbook of Mathematical Economics, North-Holland, page 1720:

Proposition 7.4 Homothecies preserve circles. That is, for any homothecy h and any circle C, h(C) is a circle as well.[…]Were we willing to do the same with homothecies, we would meet an obstruction: the composition of two homothecies is not necessarily a homothecy.

2013, Felipe Cucker, Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press, page 161:


homothety

From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).

The product of two homotheties with the same centre is a homothety with that centre.

1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:

One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.

1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:

Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ.

2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:

(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.

homothecy

isotropic scaling transformation with a fixed point


pentachoron

en-noun

pentachoron (plural pentachorons or pentachora)

pentachorons (plural)
pentachora (plural)

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From penta- (“five”) + -choron (“4-dimensional solid”), from Ancient Greek πέντε (pénte, “five”) and χῶρος (khôros, “room”).

af

A triangle becomes a tetrahedron (a type of pyramid), then a pentachoron (a hyperpyramid).

2008, George Musser, The Complete Idiot's Guide to String Theory, page 174:

Geometrically, K₃ relates to a triangle, K₄ a tetrahedron, K₅ a pentachoron, etc.

2008, Prabhakar Gupta et al., Design and Analysis of Algorithms, page 356:

The tetrahedron is a 3-simplex whose 4-simplex analog is the pentachoron, a four-dimensional body which can be orphographically ^([sic]) projected onto a quincrux (as well as a pentagram and other shapes).

2013, Caspar Henderson, The Book of Barely Imagined Beings, page 7:

(mathematics) A four-dimensional object analogous to a tetrahedron, constructed out of five tetrahedra.


Catalan solid

From Catalan (“a surname”) + solid, named for Belgian mathematician Eugène Charles Catalan.

1993, E. Heil, H. Martini, 1.11: Special convex bodies, P. M. Gruber, J. M> Wills (editors), Handbook of Convex Geometry, Volume A, page 352,
These duals are also called Catalan solids, because Catalan was the first mathematician who described all of them, cf. Brückner (1900, p. 160). Some of the Catalan solids are much older, e.g., the rhombic dodecahedron, which plays a role in crystallography (cf. chapter 37), and the rhombic triacontahedron, which is of some importance also in the theory of quasicrystals (cf. chapter 3.5).

The set of thirteen such duals is historically designated the Catalan solids. Perhaps the most striking feature of a Catalan solid is that it is composed of just one kind of face that is not a regular polygon. A face of a Catalan solid can be simply constructed by the Dorman-Luke construction [3, 4, 6, 16], which is based on a dualization process known as polar reciprocation [6], with respect to the midsphere.

2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 4:

As the most complex of the Catalan solids, the disdyakis triacontahedron has 1680 geometrical elements surrounding its axis, according to Table 1, whilst 2400 elements surround it when its faces are divided into their sectors, i.e., 720 elements are added by this division. These numbers are ten times the corresponding numbers for the simplest Catalan solid.

2009, Stephen M. Phillips, The Mathematical Connection Between Religion and Science, page 270:

(geometry) The dual polyhedron of any Archimedean solid.


pentacontagon

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From pentaconta- (“50”) + -gon (“-sided”), from Ancient Greek πεντήκοντᾰ (pentḗkontă, “50”) and γωνία (gōnía, “corner”).


gömböc

From Hungarian gömböc (“short, plump person; gömböc”).

(geometry) A convex shape which, if made of a uniformly dense material, has one stable equilibrium orientation and one unstable equilibrium orientation.


saddle point

(geometry) A point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane.


hypoellipse

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(geometry) A superellipse with an exponent (shape parameter) smaller than that of the ellipse, i.e. less than two.


-angle

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(geometry, of a two-dimensional shape) having the specified number of internal angles


isoperimetric

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(geometry) Having the same perimeter; applied to the problem of finding a plane figure of the largest possible area whose boundary has a specified length


hyperkähler

(geometry, of a manifold) Being a quaternionic analogue of a Kähler manifold.


constructible

destructible

antonym(s) of “capable of being constructed”

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(geometry, of a regular polygon) That can be constructed in a plane using only a pair of compasses and a straightedge.


nonprimitive

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(programming, computer graphics, geometry) An object that is not a primitive.


pons asinorum

From New Latin pons asinorum, from Latin pōns (“bridge”) + genitive plural of asinus (“donkey”). Literally, “bridge of donkeys”.

[H]e had scarce advanced beyond the Pons Asinorum, when his ardour abated, the test of truth by demonstration did not elevate him to those transports of joy with which his preceptor had regaled his expectation; and before he arrived at the fortieth and seventh proposition, he began to yawn drearily […].

1751, [Tobias] Smollett, The Adventures of Peregrine Pickle […], volume (please specify |volume=I to IV), London: Harrison and Co., […], →OCLC:

(geometry) A proposition in Euclid stating that the angles at the base of an isoceles triangle are equal.


-choron

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From Ancient Greek χῶρος (khôros, “room”).

(geometry) Used to form the names of 4-dimensional solids bounded by a certain number of cells/polyhedra (polychora).


holyhedron

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John Conway of Princeton University offered a reward in the 1990s to anyone producing a holyhedron, a polyhedron with a finite number of faces and with a hole in every face. […] Conway had predicted that someone will eventually find a holyhedron with fewer than 100 faces.

1969, Charles Miller, Vern Heeren, John Hornsby, Margaret Morrow, Jill Van Newenhizen, Mathematical Ideas, 11th edition:

(geometry) A polyhedron with a finite number of faces and with a polygonal hole in every face, the holes' boundaries sharing no point with each other or the face's boundary.


dihedral angle

Any two dihedral angles are to one another as the angles contained by perpendiculars drawn as in the last proposition.

1830, Pierce Morton, Geometry, Plane, Solid and Spherical, London: Baldwin and Cradock, page 136:

The remaining dihedral angles are the source of essentially all the interesting variability in protein conformation.

1981, Jane S. Richardson, “The Anatomy and Taxonomy of Protein Structure”, in C. B. Afinson, John T. Edsall, Frederic M. Richards, editors, Advances in Protein Chemistry, volume 34, page 173:

The significance of small dihedral angles is readily apparent in Fig. 6.20, where the shape of the intersection is shown for angles of 10° and 1°.

2009, Reza Abbaschian, Lara Abbaschian, Robert E. Reed-Hill, Physical Metallurgy Principles, Cengage Learning, page 176:

(geometry) The angle between two planes.


catenoid

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(geometry) A three-dimensional surface formed by rotation of a catenary

懸鏈面 /悬链面

Three-dimensional surface formed by rotation of a catenary


cuboctahedral

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(geometry) Of, pertaining to, or having the form of a cuboctahedron


nestohedron

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generalized permutahedron
generalized permutahedron

(geometry) For a building set B, the Minkowski sum of the simplices Δ_S as S ranges over B. (Here Δ_S is the standard simplex of S, i.e., the convex hull of the (nonzero endpoints of the) standard unit vectors eᵢ for i in S.) Every nestohedron is a generalized permutahedron.


supercircle

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(geometry) A special case of a superellipse having equal semimajor and semiminor axes.


umbilic

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subfigure

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(geometry) A figure (geometric form) that is part of another.


cylindricity

en-noun

cylindricity (countable and uncountable, plural cylindricities)

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

(uncountable, geometry) The quality of being cylindrical.

(countable, geometry) A three-dimensional geometric tolerance that controls how much a feature can deviate from a perfect cylinder.


cantellation

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(geometry) An operation in any dimension that cuts a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex.


geometrodynamics

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

(physics) Any of several reformulations of general relativity that attempt to describe spacetime and associated phenomena completely in terms of geometry.


pseudosphere

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(geometry) A surface generated by rotating a tractrix about its asymptote; a tractricoid

(geometry) Any of various surfaces with constant negative Gaussian curvature.


projectivity

projectivity (countable and uncountable, plural projectivities)

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

projective transformation
projective transformation

(geometry) projective transformation, homography


Apollonian circle

Apollonian circle (plural Apollonian circles)

(geometry) Any circle in two families of circles such that every circle in the first family intersects every circle in the second family orthogonally and vice versa.


hemiellipse

hemiellipses (plural)
hemi-ellipse (alternative)

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(geometry) A shape obtained by cutting an ellipse in half along one of its axes


homography

homography (countable and uncountable, plural homographies)

/həʊˈmɒɡɹəfɪ/

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A homography on a real projective plane can be specified by a mapping from one set of four non-collinear points to another set of four non-collinear points. Given such a specification, then the 3-by-3 homography matrix may be computed by means of the DLT (Direct Linear Transformation) algorithm.

(geometry) An isomorphism between projective spaces that maps straight lines to straight lines.


conoid

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(geometry) A Catalan surface all of whose rulings intersect some fixed line

A parabolic conoid is a paraboloid; an elliptic conoid is an ellipsoid.

(geometry) A solid formed by the revolution of a conic section about its axis


cubically

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hexatetrahedron

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(geometry) A cube truncated by two tetrahedra


arclength

arclengths (plural)
arc length (alternative)

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


isogonal

/ʌɪˈsɒɡənəl/

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


circumcircle

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(geometry) A circle that passes through every vertex of a given triangle (or other polygon where possible).

circumferència circumscrita

a circle that passes through every vertex of a given polygon


hemiellipsoid

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(geometry) Either of the halves into which an ellipsoid is divided by a plane of symmetry


glome

Borrowed from Latin glomus (“a ball”). Compare globe.

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

(geometry) A hypersphere in 4-dimensional Euclidean space defined as the set of all points that are at a given distance from a given point, also called a 3-sphere.


truncus

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From Latin truncus. Doublet of tronk and trunk.

(geometry) A curve in the Cartesian plane consisting of all points (x,y) satisfying an equation of the form f(x)=a/(x+b)²+c where a, b, and c are given constants.


tetradecagonal

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(geometry) Having the form of a tetradecagon


reptation

reptation (countable and uncountable, plural reptations)

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(geometry) The motion of one plane figure around another, so that the longest diameter of one shall come into line with the shortest of the other.


full circle

по́лный цикл

full turn back to the original direction or orientation

Arcs are measured in degrees, with 360° in the full circle.

2007, Carolyn C. Wheater, Geometry, page 193:


isogonic

en-adj

isogonic (comparative more isogonic, superlative most isogonic)

more isogonic (comparative)
most isogonic (superlative)

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


quindecagonal

quindecagonal (comparative more quindecagonal, superlative most quindecagonal)

more quindecagonal (comparative)
most quindecagonal (superlative)

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

(geometry) Shaped like a quindecagon; fifteen-sided.


quasiregular

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The lattice points that lie in this plane are the vertices of the regular tessellation {3, 4} of equilateral triangles, and the other points just mentioned are the vertices of the quasiregular tessellation #92;begin#123;Bmatrix#125;3#92;#92;4#92;end#123;Bmatrix#125; of triangles and hexagons [9, p. 60].

1981, H. S. M. Coxeter, “The Derivation of Schoenberg's Star Polytopes from Schoute's Simplex Nets”, in Chandler Davis, Branko Grünbaum, F.A. Sherk, editors, The Geometric Vein: The Coxeter Festschrift, page 151:

There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.

1996, Wolfgang Schueller, The Design of Building Structures, page 540:

2007, V. A. Blatov, O. Delgado-Friedrichs, M. O'Keeffe, D. M. Proserpio, Periodic nets and tilings: possibilities tor analysis and design of porous materials: Proceedings of the 15th International Zeolite Conference, Ruren Xu, Jiesheng Chen, Zi Gao, Wenfu Yan (editors), From Zeolites to Porous MOF Materials, page 1642,
If we allow the coordination figure to be a quasiregular polyhedron (a polyhedron with one kind of vertex and edge, but two kinds of face) there is just one possibility compatible with translational symmetry – a cuboctahedron.

Two semiregular polyhedra are classified as so-called quasiregular polyhedra. They have two kinds of faces, and each face of one kind is entirely surrounded by faces of the other kind.

2007, Istvan Hargittai, Magdolna Hargittai, Symmetry through the Eyes of a Chemist, page 89:

(geometry, of a polyhedron or tessellation) That is semiregular with regular faces of precisely two types that alternate around each vertex.


snub cube

From cubus simus, Kepler's name for this solid.

1995, R. H. Hardin, N. J. A. Sloane, Codes (Spherical) and Designs (Experimental), Robert Calderbank (editor), Different Aspects of Coding Theory: American Mathematical Society Short Course, Proceedings of Symposia in Applied Mathematics, Volume 50, page 183,
Robinson [67] showed in 1961 that the best packing of 24 points is achieved by the vertices of a regular snub cube, one of the Archimedean solids (cf. [20]).

1996, William P. Schaefer, The Snub Cube in the Glanville Courtyard of the Beckman Institute at the California Institute of Technology, The Chemical Intelligencer, reprinted in 2015, Balazs Hargittai, István Hargittai (editors), Culture of Chemistry: The Best Articles on the Human Side of 20th-Century Chemistry from the Archives of the Chemical Intelligencer, page 55,
A wooden model, though, showed that with a sufficiently strong flow, the entire surface of the solid could be wet; we were given the go-ahead to install a five-foot-tall, granite snub cube in the fountain.

Two of these are chiral pairs, the dextro snub cube and its chiral partner, the laevo snub cube; the third is the regular orbit of T_d point symmetry, while the fourth is the regular orbit of Tₕ symmetry.

2005, Charles M. Quinn, Patrick Fowler, David Redmond, Computational Quantum Chemistry II: The Group Theory Calculator, page 44:

equilateral triangle
equilateral triangle

(geometry) An Archimedean solid with thirty-eight faces, of which six are squares (no two of which share a vertex) and thirty-two are equilateral triangles.

cubus sinus

polyhedron with 6 square and 32 triangular faces


Riemannian manifold

en-noun

Riemannian manifold (plural Riemannian manifolds)

Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian.

риманово многообразие

real, smooth differentiable manifold equipped with a Riemannian metric

By definition, a Riemannian manifold M has at each point p a tangent space T#95;pM equipped with a positive-definite inner product, g#95;p; information about these inner products is encoded in the Riemannian metric tensor, g.

In this chapter we extend the study of eigenvalues to Riemannian manifolds whose curvature may not be constant, but is, nevertheless, bounded.

1984, Isaac Chavel, Eigenvalues in Riemannian Geometry, Academic Press, page 55:

Further, a much harder theorem, due to J. Nash [31], says that a separable Riemannian manifold of dimension d can be isometrically embedded in #92;textstyle#92;mathbbRᴺ with N#92;le#123;#92;tfrac 1 2#125;d(d#43;1)(3d#43;11).

2000, Daniel W. Stroock, An Introduction to the Analysis of Paths on a Riemannian Manifold, American Mathematical Society, page 165:

Before we delve into the general theory of Riemannian manifolds, we pause to give it some substance by introducing a variety of "model Riemannian manifolds" that should help to motivate the general theory.

2018, John M. Lee, Introduction to Riemannian Manifolds, 2nd edition, Springer, page 55:

(differential geometry, Riemannian geometry) A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;

differential geometry; Riemannian geometry; differential geometry; Riemannian geometry

differential geometry; Riemannian geometry; more formally

A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
(more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.