Klein geometry

en-noun

Klein geometry (plural Klein geometries)

Erlangen program
Felix Klein
Klein geometry

Named after German mathematician Christian Felix Klein (1849—1925). The concept arose from Klein's Erlangen program (published 1872).

Given a Klein geometry (G,H), the group G is called the principal group and G#x2F;H is called the space of the geometry.

The space of a Klein geometry is a smooth manifold of dimension #x5C;operatorname#x7B;dim#x7D;G-#x5C;operatorname#x7B;dim#x7D;H.

The present paper develops the general theory of non-holonomic geometries as generalizations of Klein geometries starting from a set of fundamental assumptions presented in the form of postulates.

1934, American Journal of Mathematics, volume 56, Johns Hopkins University Press, page 153:

The kernel of a Klein geometry (G,H) is the largest subgroup K of H that is normal in G. A Klein geometry (G,H) is effective if K#x3D;1 and locally effective if K is discrete. A Klein geometry is geometrically oriented if G is connected.

2006, Luciano Boi, “The Aleph of Space”, in Giandomenico Sica, editor, What is Geometry?, Polimetrica, page 91:

A careful geometric study of Klein geometries is available in [Sh97, Chapter 4].
Given a Klein geometry (G,H) we may first ask whether all of G is “visible” on G#x2F;H, i.e. whether the action #x5C;mathcal#x7B;l#x7D; of G on G#x2F;H is effective. In this case, we call the Klein geometry effective.

2009, Andreas Čap, Jan Slovák, Parabolic Geometries I, American Mathematical Society, page 49:

(differential geometry) A type of geometry (mathematical object representing a space and its spatial relationships); a homogeneous space X together with a symmetry group which represents the group action on X of some Lie group;

A type of geometry (mathematical object representing a space and its spatial relationships); a homogeneous space X together with a symmetry group which represents the group action on X of some Lie group;
(more formally) an ordered pair (G, H), where G is a Lie group and H a closed Lie subgroup of G such that the left coset space G / H is connected.


Thales's theorem

Generally attributed to Thales of Miletus.

(geometry) A theorem stating that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle.

intercept theorem
intercept theorem#English


quarter circle

(geometry) A quarter of a circle. The shape formed from an arc that is a quarter of the circumference of a circle.


polyhedrometry

(geometry) The measurement of polyhedra.


libration point

libration point (plural libration points)

(astrophysics) Synonym of Lagrange point


quindecangle

(obsolete, geometry) Synonym of quindecagon.


Aldrin cycler

From Aldrin + cycler. After Buzz Aldrin, who developed the concept and its mathematical basis. From being a cycler, a space vehicle which cycles between intercepts of two celestial bodies in their own orbits, with little or no orbital adjustments needed, on as close to pure ballistics as practicable.

(astronautics) A spacecraft which cycles between Earth and Mars, in its own orbit which intercepts both their orbits at times when the planets are at those points in their orbits; which allows transport from Earth to Mars, or vice versa.


quadriquadric

(geometry, obsolete) A curve that is the complete intersection of two quadric surfaces.


Boothian

(geometry) Of or relating to a tangential coordinate system invented by James Booth.


Poincaré ball

The equivalent of a Poincaré disk in three or more dimensions.


aikyon

(physics) An elementary particle in octonionic space


tetragonism

quadrature of the circle
quadrature of the circle

(dated, mathematics) quadrature of the circle


pentagonohedron

(geometry) Any polyhedron that has pentagonal faces.


isoperimeter

(geometry) A figure that has the same perimeter as another


homocentrical

(geometry) Alternative form of homocentric (“having the same centre”)


velary

(geometry, obsolete) Relating to a curve representing the motion of a sail blown by the wind.


Gaussian function

Gaussian function (plural Gaussian functions)

(mathematics) A function of the form f(x)=a· exp (-((x-b)²)/(2c²)) for arbitrary real-number constants a, b and non-zero c; used in statistics, signal processing, etc.


arcosh

/ˈɑː(ɹ)ˌkɒʃ/

(trigonometry) The area hyperbolic cosine function, i.e., the inverse hyperbolic cosine function.


arsinh

/ˈɑː(ɹ)ˌsaɪnʃ/

/ˈɑː(ɹ)ˌʃaɪn/

(trigonometry) The area hyperbolic sine function, i.e., the inverse hyperbolic sine function.


artanh

/ˈɑː(ɹ)ˌtænʃ/

(trigonometry) The area hyperbolic tangent function, i.e., the inverse hyperbolic tangent function.


Sumihiro's theorem

(algebraic geometry) A theorem stating that a normal algebraic variety with an action of a torus can be covered by torus-invariant affine open subsets.


Białynicki-Birula decomposition

Białynicki-Birula decomposition (plural Białynicki-Birula decompositions)

The description depends on a partial ordering of the fixed point components which arises from the Białynicki-Birula decompositions of X.

1984, Pacific Journal of Mathematics, volumes 114-115, page 149:

Section 2 describes a C*-action on Grassmann manifolds and gives the corresponding Białynicki-Birula decomposition.

1988, Mathematica Scandinavica, volume 62, page 5:

(algebraic geometry) A T-stable cellular decomposition of a smooth T-variety.


Schönhardt polyhedron

Schönhardt polyhedron (plural Schönhardt polyhedra)

Named after German mathematician Erich Schönhardt, who described it in 1928.

(geometry) The simplest non-convex polyhedron that cannot be triangulated into tetrahedra without adding new vertices.


octakishexahedron

(geometry, rare) A polyhedron with 48 faces.


superspatial

Situated or taking place above or outside the limits of space.


Barnes integral

Barnes integral (plural Barnes integrals)

They were introduced by Ernest William Barnes.

(mathematics) A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series.


busy beaver function

busy beaver function (plural busy beaver functions)

(mathematics, computing theory) The mathematical function, denoted by Σ(n), that maps each positive integer n to the number of steps required for the busy beaver among machines with two colors and n states to terminate.


Fermat curve

Named after French mathematician Pierre de Fermat (1607-1665).

homogeneous coordinate
homogeneous coordinate

(mathematics) The algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation.


halo orbit

First used by NASA mission specialist Robert W. Farquhar in 1966 for calculated orbits around the Earth-Moon L₂ point which required the use of thrusters to be made periodic.

Due to the strong hyperbolic character of the halo orbits, the stable manifold approaches the halo orbit in a very fast way. This fact means that if we are able to put the satellite in the stable manifold of a halo orbit, it will be close to the halo orbit (say at [a] few km) in a reasonable period of time.

2001, G. Gómez, À. Jorba, J. Masdemont, C.Simó, Dynamics and Mission Design Near Libration Points, Volume III, World Scientific, page 93:

2013, Yuhui Zhao, Shoucun Hu, Xiyun Hou, Lin Liu, Chapter 39: On Nominal Formation Flying Orbit with a Small Solar System Body, Rongjun Shen, Weiping Qian (editors), Proceedings of the 26th Conference of Spacecraft TT&C Technology in China, Tsinghua University Press, Springer, Lecture Notes in Electrical Engineering 187, page 395,
If the ratio of the amplitude in x-direction to γ₁ keeps unchanged (=0.155), the periods of halo orbits are almost the same (about 190 days). As a result of the stability of CRTBP and the dynamics of halo orbit formation, nominal halo orbits do not exist if the ratio is too large or too small.

Thus, the minimum possible size for halo orbits in the Sun-Earth system is approximately (240 x 660) 10³ km at L₁ and (250 x 675) 10³ km at L₂, sizes denoting the maximum excursion from the libration point in the x and y directions respectively.

2013, Daniel García Yárnoz, Joan-Pau Sanchez, Colin R. McInnes, “Chapter 21: Opportunities for Asteroid Retrieval Missions”, in Viorel Badescu, editor, Asteroids: Prospective Energy and Material Resources, Springer, page 486:

(orbital mechanics) A periodic, three-dimensional orbit about any one of the Lagrange points L₁, L₂ or L₃ of a two-body gravitational system.


runcicantellation

(geometry) The simultaneous state of runcination and cantellation.


omnitruncation

Wythoff construction
Wythoff construction

(geometry) An operation applied to a regular polytope in a Wythoff construction that creates a maximum number of facets.


Wythoff construction

Wythoff construction (plural Wythoff constructions)

Named after the Dutch mathematician Willem Abraham Wythoff (1865–1939).

(geometry) A method for constructing a uniform polyhedron or plane tiling.

Willem Abraham Wythoff
Wythoff construction


bi-elliptic transfer

bi-elliptic transfer (plural bi-elliptic transfers)

(astronautics) A type of movement of a spacecraft from one orbit to another, in which the spacecraft first raises its apoapsis to an extremely high altitude, then, at the new, higher, apoapsis, performs an engine burn to change its periapsis to that of the desired orbit, and, finally, upon reaching the new periapsis, performs a third burn to lower the eccentricity of its orbit and circularize in the desired orbit, or performs these steps in reverse to move from a higher to a lower orbit.


Ptolemy's theorem

Named after the Greek astronomer and mathematician Ptolemy.

cyclic quadrilateral
cyclic quadrilateral

(geometry) A theorem that states in a cyclic quadrilateral, the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the two pairs of opposite sides.


didodecahedron

didodecahedron (plural didodecahedra or didodecahedrons)

didodecahedra (plural)
didodecahedrons (plural)

Didodecahedrons are never seen in crystals, as predominating forms; but they are frequently met with as modifying faces, in combinations, principally in those in which the 6-sided prism predominates.

1853, “Crystallography”, in Th[omas] Forrest Betton, transl., edited by James C[urtis] Booth and William L. Faber, Elements of Chemistry. For the Use of Colleges, Academies, and Schools., 2nd edition, volume I, Philadelphia, Pa.: Clark & Hesser, translation of original by [Henri] V[ictor] Regnault, section “The six systems of crystalline forms”, subsection 3 (Hexagonal system), page 34:

[…]a pair of opposite edges of every face are parallel, so that the form shows prominent zonal relationships which are not characteristic of didodecahedra in general.

1946, F[rank] C[oles] Phillips, “The Thirty-two Classes”, in An Introduction to Crystallography, Longmans, Green and Co., part I (The External Symmetry of Crystals), pages 145–146:

(geometry) A solid with 24 faces consisting of scalene triangles.


mucube

(geometry) A regular skew apeirohedron with six squares around each vertex, formed by an infinite number of cubic cells (specifically, cubes missing two opposite faces each, around cubic empty spaces with no faces) in Euclidean 3D space.


mutetrahedron

mutetrahedron (plural mutetrahedra or mutetrahedrons)

mutetrahedra (plural)
mutetrahedrons (plural)

truncated tetrahedron
truncated tetrahedron

(geometry) A regular skew apeirohedron with six hexagons around each vertex, formed by an infinite number of truncated tetrahedron-like cells (specifically, truncated tetrahedra missing their triangle faces, with the resulting triangle-shaped holes joined to form empty spaces in the shape of faceless tetrahedra) in Euclidean 3D space.

六角六片三角孔ねじれ正多面体

ろっかくろくへんさんかくこうねじれせいためんたい


muoctahedron

muoctahedron (plural muoctahedra or muoctahedrons)

muoctahedra (plural)
muoctahedrons (plural)

truncated octahedra
truncated octahedron

(geometry) A regular skew apeirohedron with four hexagons around each vertex, formed by an infinite number of octahedron-like cells (specifically, truncated octahedra missing their square faces, and joined by the resulting square-shaped holes) in Euclidean 3D space.

六角四片四角孔ねじれ正多面体

ろっかくしへんしかくこうねじれせいためんたい


Oberth effect

(astronautics) The concept that the most efficient place for spacecraft to change velocity is at the periapsis (the lowest point of an orbit).


circumtriple

(astrophysics) orbiting around three stars or other centers.


Donaldson-Thomas theory

Donaldson-Thomas invariant
Donaldson-Thomas invariant

(algebraic geometry) The theory of Donaldson-Thomas invariants.


Donaldson-Thomas invariant

Donaldson-Thomas invariant (plural Donaldson-Thomas invariants)

Introduced in 1998 by Simon Donaldson and Richard Thomas.

Calabi-Yau threefold
Calabi-Yau manifold#English

(algebraic geometry) Given a compact moduli space of sheaves on a Calabi-Yau threefold, its Donaldson-Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class.


Calabi-Yau manifold

Calabi-Yau manifold (plural Calabi-Yau manifolds)

The name was coined by Candelas et al. (1985), after Eugenio Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978), who proved the Calabi conjecture.

(algebraic geometry) A kind of manifold having properties, such as Ricci flatness, that yield applications in theoretical physics.


Kähler manifold

Kähler manifold (plural Kähler manifolds)

Introduced by Erich Kähler in 1933, though the concept had been studied by others a few years earlier.

differential geometry
differential geometry

(differential geometry) A manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.


quasi-moon

From quasi- + moon, modeled after quasi-satellite.


obliquangular

an obliquangular triangle

(archaic, geometry) Formed of oblique angles.


ideal triangle

In hyperbolic geometry, a triangle whose vertices are all ideal; i.e. points at infinity, rather than real.


lateral surface

lateral surface (plural lateral surfaces)

(geometry) All of the sides of the object, excluding its base and top (when they exist).

سطح جانبي

all of the sides of the object, excluding its base and top (when they exist)


transition map

transition function
transition function#English

(differential geometry) Synonym of transition function.


coordinate map

Let (W#x5F;0,#x5C;psi) be a smooth coordinate chart for P, and let (E#x5F;1,#x5C;dots,E#x5F;#x7B;n-p#x7D;) be a local orthonormal frame for the normal bundle NP; by shrinking W#x5F;0 if necessary, we can assume that the coordinates and the local frame are defined on the same open subset W#x5F;0#x5C;subseteqP. Let #x5C;hat#x7B;W#x7D;#x5F;0#x3D;#x5C;psi(W#x5F;0)#x5C;subseteq#x5C;mathbb#x7B;R#x7D;ᵖ, and let NP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; be the portion of the normal bundle over W#x5F;0. The coordinate map #x5C;psi and frame (E#x5F;j) yield a diffeomorphism #x5C;hat#x7B;W#x7D;#x5F;0#x5C;times#x5C;mathbb#x7B;R#x7D;#x7B;n-p#x7D;#x5C;rightarrowNP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; defined by[…]

2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 135:

coordinate chart
coordinate chart#English

(differential geometry) Synonym of coordinate chart.


coordinate chart

coordinate chart (plural coordinate charts)

A set S#x5C;subset#x5C;mathbb#x7B;R#x7D;³ is called a regular surface if each of its points has a neighborhood in S that is diffeomorphic to an open set in #x5C;mathbb#x7B;R#x7D;². That is, for every p#x5C;inS, there exists a neighborhood, V, of p in S, an open set U#x5C;subset#x5C;mathbb#x7B;R#x7D;², and a diffeomorphism #x5C;sigma#x3A;U#x5C;rightarrowV. Such a diffeomorphism #x5C;sigma is called a surface patch or a coordinate chart. A collection of surface patches that together cover all of the points of S is called an atlas for S.

2016 September 30, Kristopher Tapp, Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 125:

(differential geometry) A homeomorphism from a local neighborhood around a point on a topological n-manifold in a Banach space to an n-dimensional Banach space (typically a subspace of the space the manifold is embedded in).


Weierstrass function

Weierstrass function (plural Weierstrass functions)

(mathematics) A real-valued function that is continuous everywhere but differentiable nowhere.


clear the neighborhood

en-verb

clear the neighborhood (third-person singular simple present clears the neighborhood, present participle clearing the neighborhood, simple past and past participle cleared the neighborhood)

clears the neighborhood (present singular third-person)
clearing the neighborhood (participle present)
cleared the neighborhood (participle past)
cleared the neighborhood (past)

Clearing the neighborhood is one of three necessary criteria for a celestial body to be considered a planet in the Solar System, according to the definition adopted in 2006 by the International Astronomical Union.

(astronomy, of a celestial body) To become gravitationally dominant, such that there are no other bodies of comparable size within its orbit, other than its natural satellites or those otherwise under its gravitational influence.


radiodrome

Greek ῥᾴδιος rhā́idios 'easier' + δρόμος drómos 'running'. Not related to radio- as in radioactive.

A pursuit curve, in which the thing being pursued is moving at constant velocity.


trisectrix

en-noun

trisectrix (plural trisectrices or trisectrixes)

trisectrices (plural)
trisectrixes (plural)

A type of curve that is useful for trisecting the angle.


inellipse

(geometry) An ellipse inscribed in a triangle.


pursuit curve

(geometry) A geometrical model which simulates the path taken by a pursuer in the course of its pursuit.


hippopede

Borrowed from Ancient Greek ἱπποπέδη (hippopédē, “horse fetter”).

bor+

A plane curve defined by the equation (x²+y²)²=cx²+dy², where it is assumed that c>0 and c>d.


octiamond

(geometry) A polyiamond made up of eight triangles.


cylindroidal

en-adj

cylindroidal (comparative more cylindroidal, superlative most cylindroidal)

more cylindroidal (comparative)
most cylindroidal (superlative)

(geometry) Having the form of a cylindroid.


Hohmann transfer

en-noun

Hohmann transfer (plural Hohmann transfers)

Named after Walter Hohmann, the German engineer who described it.

(astronautics) An elliptical orbit used to transfer a spacecraft between two circular orbits of different altitudes in the same plane, with the periapsis of the orbit being tangent to the smaller circular orbit and its apoapsis being tangent to the larger circular orbit.


inverse tangent

inverse tangent (plural inverse tangents)


grand 600-cell

(geometry) A regular star 4-polytope with Schläfli symbol {3,3,5/2}


tridecagram

A star polygon that has thirteen vertices.


great dodecahedron

great dodecahedron (plural great dodecahedra or great dodecahedrons)

great dodecahedra (plural)
great dodecahedrons (plural)

(geometry) A Kepler solid, with the Schläfli symbol {5,5/2}.


hyperbolic dodecahedron

hyperbolic dodecahedron (plural hyperbolic dodecahedrons)

(hyperbolic geometry) A hyperbolic version of the Euclidean dodecahedron.


great icosahedron

great icosahedron (plural great icosahedra or great icosahedrons)

great icosahedra (plural)
great icosahedrons (plural)

Kepler-Poinsot polyhedra
Kepler-Poinsot polyhedra

(geometry) One of four Kepler-Poinsot polyhedra with Schläfli symbol {3,5⁄2}.


Archimedes' constant

(mathematics, chiefly historical) Synonym of pi


Cavalieri's principle

method of indivisibles
method of indivisibles

(geometry) A development of the method of indivisibles, dealing with two-dimensional area or three-dimensional volume based on the intersections of lines or planes surrounding a region. It was an early step toward integral calculus.


wallpaper group

wallpaper group (plural wallpaper groups)

(geometry) A mathematical group that classifies two-dimensional repeating patterns based on their symmetries.


hexadecahedroid

(geometry) The 16-cell or hexadecachoron.


Alexander horned sphere

Alexander horned sphere (plural Alexander horned spheres)

(topology) A pathological object, a certain embedding of a sphere in three-dimensional Euclidean space, obtained by various modifications of a torus.


Varignon's theorem

Named after French mathematician Pierre Varignon.

Varignon parallelogram
Varignon parallelogram

(geometry) A statement in Euclidean geometry that deals with the construction of a particular parallelogram (the Varignon parallelogram) from an arbitrary quadrilateral.


planigon

(geometry) A convex polygon that can fill the plane with only copies of itself.


unit disk

A set of points on a plane whose distance from a given point is less than or equal to one.


surjective function

surjective function (plural surjective functions)


nonintersector

(geometry) That which is not an intersector.


square degree

(geometry) A unit of solid angle equal to π²/32400 steradians


tricuspal

(geometry, dentistry) Consisting of, or relating to, three cusps.


heliosynchronous orbit

heliosynchronous orbit (plural heliosynchronous orbits)

sun-synchronous orbit
sun-synchronous orbit

(astrodynamics) A sun-synchronous orbit.


sun-synchronous orbit

sun-synchronous orbit (plural sun-synchronous orbits)

(astrodynamics) A nearly polar orbit in which a satellite passes over the surface of a planet maintaining the same local mean solar time.


kissing number

(geometry) For a given space, the maximum number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere.


Pappian

a Pappian plane

Pappus's hexagon theorem
Pappus's hexagon theorem

(geometry) For which Pappus's hexagon theorem is valid.


icositrigon

(geometry) A polygon with 23 sides and 23 angles.


hypersolid

(geometry) A solid that extends into hyperspace, having more than three dimensions.


hypertetrahedron

(geometry) An analog of a tetrahedron that extends into hyperspace, having more than three dimensions.


hyperprism

(geometry) A prism that extends into hyperspace, having more than three dimensions.


oblique pyramid

oblique pyramid (plural oblique pyramids)

(geometry) A nonright pyramid, where the apex is not centered over the base.


oblique reflection

oblique reflection (plural oblique reflections)

(geometry) In Euclidean geometry, an ordinary reflection not requiring that the reflection be performed using perpendiculars.


Keller graph

(geometry) Any of a certain family of graphs related to Keller's conjecture, such that the vertices of the Keller graph of dimension n are the 4ⁿ elements (m₁,...,mₙ) where each m is 0, 1, 2, or 3, and two vertices are joined by an edge if they differ in at least two coordinates and differ by exactly two in at least one coordinate.


Keller's conjecture

The conjecture was introduced by Ott-Heinrich Keller (1930).

(geometry) The conjecture that, in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.


focaloid

(geometry) A shell bounded by two concentric, confocal ellipses (in two dimensions) or ellipsoids (in three dimensions).


inflectional tangent

inflectional tangent (plural inflectional tangents)

(differential calculus, differential geometry) A tangent to a curve at a point of inflection.

differential calculus; differential geometry; differential calculus; differential geometry


parallel transport

parallel transport (countable and uncountable, plural parallel transports)

(geometry) A way of transporting geometrical data along smooth curves in a manifold.


Star of Lakshmi

"Lakshmi" from the Hindu god Lakshmi and the "star" word in the noun denotes the octagram.

(geometry) A special octagram, a regular compound polygon, represented by Schläfli symbol {8/2} or 2{4}, made from two congruent squares with the same center at 45° angles.


Boerdijk-Coxeter helix

Named after H. S. M. Coxeter and A. H. Boerdijk.

(geometry) A linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices.


Weaire-Phelan structure

Weaire-Phelan structure (plural Weaire-Phelan structures)

Named after Denis Weaire and Robert Phelan, who in 1993 found that this structure was a better solution to the Kelvin problem of tiling space by equal-volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.

(geometry) A three-dimensional structure representing an idealized foam of equal-sized bubbles, with two different shapes.


SFT

sparse Fourier transform
w:sparse Fourier transform

(mathematics) Initialism of sparse Fourier transform.


STFT

short-time Fourier transform
w:short-time Fourier transform

(mathematics) Initialism of short-time Fourier transform.


Tschirnhausen cubic

Tschirnhausen cubic (plural Tschirnhausen cubics)

Named after Ehrenfried Walther von Tschirnhaus (1651–1708), German mathematician, physicist, physician, and philosopher. The name was first used in a 1900 paper by R. C. Archibald.

(geometry) A plane curve defined, in its left-opening form, by the polar equation r=a sec ³(θ/3) where sec is the secant function.


tangent line

(differential geometry) Synonym of tangent (“straight line touching a curve at a single point without crossing it there”).


hexahectaenneacontakaiheptagon

Analysable as hexahecta- (“six hundred”) (from hexa- + hect(a)-) + enneaconta- (“ninety”) (from ennea- + the common element in Ancient Greek ἑξήκοντα (hexḗkonta, “sixty”), τεσσαράκοντα (tessarákonta, “forty”), etc.) + Ancient Greek καί (kaí, “and”) + hepta- (“seven”) + -gon.
Coined humorously to describe the shape of the US state of Colorado.

der

Colorado is actually a hexahectaenneacontakaiheptagon, meaning it has 697 sides, according to a 2018 bigthink.com article and Kutztown University's math whizzes who create names for polygons.

2019 October 16, James Burky, “Rectangle state? Nope. Colorado has 697 sides, not four.”, in The Denver Post, archived from the original on 2023-01-08:

A study in 2018 suggested that as a result of the challenges of surveying in the nineteenth century, Colorado has no fewer than 697 sides, technically making it a "hexahectaenneacontakaiheptagon."

2020, Derek Everett, Colorado Day by Day, Boulder, CO: University Press of Colorado, →ISBN, page 212:

The state of Colorado may look like a rectangle (four straight sides, four right angles) but it actually has 697 sides, making it a hexahectaenneacontakaiheptagon.

2020, Bathroom Readers' Institute, Uncle John's Greatest Know on Earth Bathroom Reader, San Diego, CA: Portable Press, →ISBN:


kaleidocycle

(geometry) A flexible polyhedron connecting six tetrahedra (or disphenoids) on opposite edges into a cycle.


Lemoine point

The French mathematician Émile Lemoine proved the existence of such points in 1873.

(geometry) The intersection of the three symmedians of a triangle.


spherical triangle

en-noun

spherical triangle (plural spherical triangles)

If the three sides of a spherical triangle be each of them equal to a quadrant, the polar triangle will coincide with it; for each of the angular points will be the pole of the side opposite to it.

1830, Pierce Morton, Geometry, Plane, Solid, and Spherical, in Six Books, Baldwin and Craddock, page 189:

570. Theorem. The sum of the sides of a spherical triangle may be anything between 0 and a circumference.

1876, Edward Olney, A Treatise on Special Or Elementary Geometry, Sheldon & Company, page 220:

1893, Crossley William Crosby Barlow, George Hartley Bryan, Elementary Mathematical Astronomy, W. B. Clive, page v,
A spherical triangle, like a plane triangle, has six parts, viz., its three sides and its three angles. The sides are generally measured by the angles they subtend, so that the six parts are all expressed as angles.
Any three parts suffice to determine a spherical triangle, but there are certain "ambiguous cases" when the problem admits of more than one solution. The formulæ required in solving spherical triangles form the subject of Spherical Trigonometry, and are in every case different from the analogous formulæ in Plane Trigonometry. There is this further difference, that a spherical triangle is completely determined if its three angles are given.

The angles in a spherical triangle do not have to add up to 180 degrees. It is possible for a spherical triangle to have 3 right angles.

2012, Daniel Zwillinger, CRC Standard Mathematical Tables and Formulae, 32nd edition, Taylor & Francis (CRC Press / Chapman & Hall), page 218:

(geometry, spherical geometry) A triangle, described on the surface of the sphere, whose each side is an arc of some great circle.

Kugeldreieck

Triangle on the surface of a sphere, whose sides are arcs of great circles


dekeract

(mathematics) A ten-dimensional hypercube


nonant

Borrowed from Latin nōnum, accusative singular of nōnus (“ninth part of something, ninth”).

(geometry) One ninth of a circle or disc; a sector with an angle of 40°.


(geometry) A cube in four dimensions or four-dimensional space; a tesseract, 8-cell or octachoron; made of eight cubical cells or eight cubes.


scalenon

(geometry, obsolete) A scalene triangle.


pentille

(geometry) A tessellation of the plane consisting of irregular pentagons.


monohedrally

The extent of our ignorance is further illustrated by the fact that we do not know all the different shapes of convex pentagons which will tile the plane monohedrally.

1987, Branko Grünbaum, G[eoffrey] C[olin] Shephard, Tilings and Patterns, New York, N.Y.: W. H. Freeman and Company, →ISBN, page 22:

(geometry) In a monohedral manner; involving only copies of the original tile (allowing for translation, rotation, and reflection).


monotile

In the following section we will describe families of tilings by a curious three-dimensional aperiodic monotile whose matching rule — for some values of its parameter — is weak but not strong.

1995, Marjorie Senechal, Quasicrystals and Geometry, Cambridge, Cambridgeshire: Cambridge University Press, →ISBN, page 208:

And I am sorry I never delivered on the four-dimensional Poultry design. It turns out John Horton Conway found four-dimensional and five-dimensional aperiodic monotiles sixty years ago, but it's not too well documented.

1997, Rudy Rucker, Freeware (Ware Tetralogy; 3), New York, N.Y.: Avon Books, →ISBN, page 69:

This naturally led to serious rumination about the possible existence of a single tile, or monotile, that forces non-periodic global structure.

2007 March, Joshua E. S. Socolar, “More ways to tile with only one shape polygon”, in The Mathematical Intelligencer, volume 29, number 2, New York, N.Y.: Springer, →DOI, →ISSN, →OCLC, page 33:

An aperiodic monotile never repeats a formation, no matter how long the pattern.

2023 April 4, Matthew Cantor, “'The miracle that disrupts order': mathematicians invent new 'einstein' shape”, in The Guardian, London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 2023-04-04:

(geometry) A prototile tiling monohedrally; any shape able to completely tile some space on its own (allowing for translation, rotation, and reflection).


duocylinder

(geometry) A geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks, and analogous to a cylinder in 3-space.


ex-tangential

(geometry) Pertaining to external tangents.


n-sphere

An n-dimensional hypersphere: the 2-sphere is a circle, the 3-sphere is the usual sphere, the 4-sphere is a glome, etc.


goat grazing problem

goat grazing problem (plural goat grazing problems)

The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?

The same problem generalized to any number of dimensions: given a unit n-sphere (n-dimensional hypersphere) S, and a point P on the edge of S, what is r such that exactly one-half of the space (content) within S, is within distance r of P?


goat problem

goat grazing problem
goat grazing problem#English


direction vector

direction vector (plural direction vectors)

Coordinate term: position vector

(geometry) A unit vector used to represent spatial direction, commonly denoted as d.


Gauss-Codazzi equation

Gauss-Codazzi equation (plural Gauss-Codazzi equations)

Named after Carl Friedrich Gauss and Delfino Codazzi.

pseudo-Riemannian manifold
pseudo-Riemannian manifold

(geometry) Any of a group of fundamental formulas in Riemannian and pseudo-Riemannian geometry that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.


Hjelmslev transformation

Hjelmslev transformation (plural Hjelmslev transformations)

(geometry) A method for mapping an entire hyperbolic plane into a circle with a finite radius.


Petersen-Morley theorem

Named after Johannes Trolle Petersen (later Johannes Hjelmslev) and Frank Morley.

(geometry) A theorem stating that, if a, b, c are three general skew lines in space, if a′, b′, c′ are the lines of shortest distance respectively for the pairs (b,c), (c,a) and (a,b), and if p, q and r are the lines of shortest distance respectively for the pairs (a,a′), (b,b′) and (c,c′), then there is a single line meeting at right angles all of p, q, and r.


hyperparallel

Two hyperparallel lines have one and only one common perpendicular.

1995, Howard Eves, College Geometry, page 246:

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

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

In order that two distinct lines K and L be hyperparallel it is necessary and sufficient that they lie in one plane and that there exists a line M intersecting both of them perpendicularly.

2018, Karol Borsuk, Wanda Szmielew, Foundations of Geometry, page 292:

(geometry) In hyperbolic geometry, lines that do not intersect in a common point in the plane and do not intersect at a common limit point at infinity, but rather, occur outside the limit set by parallel lines which intersect at infinity.


hyperboloid of revolution

hyperboloid of revolution (plural hyperboloids of revolution)

(geometry) The surface generated by rotating a hyperbola around one of its principal axes.


Cartesian equation

Cartesian equation (plural Cartesian equations)

(geometry, algebra) An equation that describes a line or plane in terms of the relationship between the coordinates on the axes involved.


Minkowski-Bouligand dimension

Minkowski-Bouligand dimension (plural Minkowski-Bouligand dimensions)

Named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.

(geometry) A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer.


glide reflection

glide reflection (countable and uncountable, plural glide reflections)

Thus every function of the form eⁱᵃz + c is the composition of a translation with a reflection and so it is a glide reflection.

1993, Saul Stahl, The Poincaré Half-plane: A Gateway to Modern Geometry, Jones & Bartlett Learning, →ISBN, page 136:

That turns out to have one small spaceship, moving diagonally up and left at c/14 with period 14 (glide reflection at generation 7):

1995 November 12, Rich Holmes, “Totalistic spaceships”, in comp.theory.cell-automata (Usenet):

Footprints along a line have glide reflection symmetry.

2004, Dorothy Koster Washburn, Donald W. Crowe, Donald Warren Crowe, Symmetry Comes of Age: The Role of Pattern in Culture, University of Washington Press, →ISBN, page 6:

(geometry) A transformation consisting of a reflection followed by a translation along the same line.


Margulis lemma

(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (the Margulis constant), the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such).


Desargues's theorem

(geometry) A theorem stating that two triangles are in perspective axially if and only if they are in perspective centrally.


R-pentomino

(geometry) A particular five-square polyomino.

I came up with an implementation of an algorithm on my Sparcstation 1 that does all 1103 generations of the R-pentomino, including the gliders, in 1.3 seconds (no display), and runs o.....o. ..o...o. ..o..o.o .o.o.... (a pattern by Wainright recommended to me by Gosper) out to 10,000 generations in 45 seconds (again, without display).

1990 January 15, Paul Dietz, “Gosper's Algorithm for Life”, in comp.theory.cell-automata (Usenet):

I've finisher debugging the code, and it works -- that is to say, its final configuration for the R-pentomino is the same as the one in my books. (It's my guess that the R-p will find any bug in any life program, no matter how obscure.)

1990 June 8, Robert Herrell, “Life without bounds”, in comp.theory.cell-automata (Usenet):

This explosive collision is "perturbed" by the permanent parts of the reflector so that at generation 242, the destroyed block is restored, a glider is released in the reverse direction, an r-pentomino is produced some distance from the stage, and a beehive is left in an awkward position close to the block.

1996 November 19, Paul Callahan, “Glider reflector in Life”, in comp.theory.cell-automata (Usenet):

(cellular automata) The methuselah based on this polyomino that, in Conway's Game of Life, has a lifespan of 1,103 generations.


Darboux's theorem

(differential geometry) A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another.


paraboloid of revolution

paraboloid of revolution (plural paraboloids of revolution)

surface of revolution
surface of revolution

(geometry) A surface of revolution formed by revolving a parabola around its axis.


versed cosine

trigonometric function
trigonometric function

(trigonometry) The trigonometric function 1 + cos(x).


semiminor axis

Coordinate term: semimajor axis

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

demi-petit axe

half of the major axis of a circle or ellipse


Mojette transform

Mojette transform (plural Mojette transforms)

(geometry) A discrete and exact version of the Radon transform, using only additions and subtractions, and having applications in medical tomography, cryptography, etc.


lune of Hippocrates

lune of Hippocrates (plural lunes of Hippocrates)

(geometry) A lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.


midpoint theorem

A theorem stating that if the midpoints of two sides of a triangle are connected, the resulting line segment will be parallel to the third side and have half of its length.


hectohedron

hectohedron (plural hectohedra or hectohedrons)

hectohedra (plural)
hectohedrons (plural)

For quotations using this term, see Citations:hectohedron.

(rare, geometry) A polyhedron with one hundred faces.


intercept theorem

(geometry) An important elementary theorem about the ratios of various line segments that are created if two rays with a common starting-point are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles.


Moser's worm problem

Formulated by the Austrian-Canadian mathematician Leo Moser in 1966.

(geometry) An unsolved problem asking for the region of smallest area that can accommodate every plane curve of length 1, i.e. the curve can be rotated and translated to fit inside the region (which in some variations of the problem is restricted to be convex).


Brocard circle

Named after Henri Brocard (1845–1922), French mathematician.

(geometry) A circle that passes through the circumcenter and symmedian of a given triangle, and is centered at the midpoint of the line segment joining them.


Japanese theorem

A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.


Varignon parallelogram

Varignon parallelogram (plural Varignon parallelograms)

(geometry) The parallelogram involved in Varignon's theorem, whose corners are the midpoints of the sides of an arbitrary quadrilateral.


Wallace line

Named after William Wallace, who published the concept in 1799.


Simson line

Named after Robert Simson, though it had been published prior to his work.

(geometry) Given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P.


folium of Descartes

(geometry) An algebraic curve defined by the implicit equation x³+y³-3axy=0.


pyramidoidal

en-adj

pyramidoidal (comparative more pyramidoidal, superlative most pyramidoidal)

more pyramidoidal (comparative)
most pyramidoidal (superlative)


rocket equation

The equation for how much delta-v a rocket produces: Δv = vₑ ln(m₀/m₁); where Δv is delta-v, vₑ is effective exhaust velocity, ln is the natural log function, m₀ is initial mass of the rocket, and m₁ is final mass of the rocket.


Moufang plane

(geometry) A type of projective plane whose every line is a translation line.


Pappus's hexagon theorem

Attributed to the Ancient Greek mathematician Pappus of Alexandria (c. 290–c. 350 AD).

(geometry) A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon AbCaBc.


myriahedron

en-noun

myriahedron (plural myriahedrons or myriahedra)

myriahedrons (plural)
myriahedra (plural)

For quotations using this term, see Citations:myriahedron.

(geometry) A polyhedron with 10,000 faces.


kisrhombille

(geometry, rare) A uniform tiling of rhombic faces divided by central points into four triangles.


undecahedron

undecahedron (plural undecahedrons or undecahedra)

undecahedrons (plural)
undecahedra (plural)

(geometry) A polyhedron with eleven faces.


pentacontahedron

pentacontahedron (plural pentacontahedrons or pentacontahedra)

pentacontahedrons (plural)
pentacontahedra (plural)

From Ancient Greek πεντήκοντα (pentḗkonta) + -hedron.

suffix

(geometry) A polyhedron with fifty faces.


monohedron

This is a reflection of the fact that the monohedron collapses asymptotically to a line (along the w₁-axis) when T -> Tₜ (t -> 0) (Widom, 1975c).

1972, Cyril Domb, M. S. Green, Joel Louis Lebowitz, Phase Transitions and Critical Phenomena - Volume 9, page 112:

(geometry) A solid figure with a single continuous surface (face) and no edges, such as a torus or spheroid.


silver ratio

(geometry) The irrational number (approximately 2.414), which is equal to the sum of its own reciprocal and two. It equals one plus the square root of two (1 + √).


duocylindrical

en-adj

duocylindrical (comparative more duocylindrical, superlative most duocylindrical)

more duocylindrical (comparative)
most duocylindrical (superlative)

(geometry) Of or pertaining to a 4-dimensional object having the shape of a duocylinder.


faithfully flat

(algebraic geometry, of a morphism of schemes) Flat and surjective.


zero locus

(algebraic geometry, of a polynomial, or, more generally, a function) The set of points (usually in affine or projective space, but more generally in the domain of the function) where the given polynomial (or function) takes the value zero.


affine scheme

locally ringed space
locally ringed space

(algebraic geometry) An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring.


distinguished open set

en-noun

distinguished open set (plural distinguished open sets)

(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring.


vanishing locus

(algebraic geometry) Synonym of zero locus.


structure sheaf

structure sheaf (plural structure sheaves)

(sheaf theory, algebraic geometry) The sheaf associated to a ringed space.


B-sheaf

(sheaf theory, algebraic geometry) A kind of partial, simpler to describe sheaf which can be extended into a sheaf (and which is, in a technical sense, equivalent to that sheaf). For a formal definition, see B-sheaf on Wikipedia.Wikipedia.


quasi-projective

From quasi- + projective, the sense being that projective varieties are closed subsets of projective space while quasi-projective varieties are only required to be locally closed, a strictly weaker condition. The second, scheme-theoretic sense generalizes the first.

(algebraic geometry, of a variety) Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set.

(algebraic geometry, of a scheme) Comprising an open subscheme of a projective scheme


elliptize

en-verb

elliptize (third-person singular simple present elliptizes, present participle elliptizing, simple past and past participle elliptized)

elliptizes (present singular third-person)
elliptizing (participle present)
elliptized (participle past)
elliptized (past)

We resorted, instead, to depositing on a test flat near the mirror being elliptized.

1949, Albert Vinicio Baez, Principles of X-ray Optics and the Development of a Single Stage X-ray Microscope, Stanford University, page 132:

When a rotator cuff tear was present, the degenerative zone was elliptzed and typically a side-to-side repair was performed.

1991, Lonnie Paulos, James E. Tibone, editors, Operative Techniques in Shoulder Surgery, Aspen Publishers, page 86:

Note that least-square discretizations are also equivalent to making the convection terms elliptic; another way to ‘elliptize’ convection was derived from the Lax—Wendroff scheme by Lerat et al. (1982).

1996, Roger Peyret, editor, Handbook of Computational Fluid Mechanics, Academic Press, page 9:

The basic configuration was optimized for a 10 arcmin FoV at a Cassegrain focus issued from a four-segment spherical primary obtained by replication, a spherically polished secondary elliptized by partial vacuum (g=1) and a doublet-lens corrector.

1998, Larry M. Stepp, editor, Advanced Technology Optical/IR Telescopes VI, volume 3352, SPIE, page 767:

Thus a unified approach to both problems suggests itself. Following an idea of R. Picard (1985) we do it in such a way that one operator structures the null space of the other. Thus the operators mutually ‘elliptize’, simplifying the presentation.

2013 July, Rolf Leis, Initial Boundary Value Problems in Mathematical Physics, Dover Publications, page 170:

Although in almost all cases the orbits of the inner planets should remain within a certain range of distances from each other; in a "probability" estimated (in the models) at a few%, it is possible that the orbits elliptize enough to intersect and cause a catastrophic destabilization of the orbits of the inner planets.

2024 May, Georges Ballin, The Bacterium that will kill the Earth "the Man", [self-published], page 21:

(ergative, uncommon) (To cause) to become elliptic or elliptical.


trisectible

(geometry) Able to be divided into three equal angles using a compass and straightedge.


pentasectible

(geometry) Able to be divided into five equal angles using a compass and straightedge.


trisectability

(geometry) Ability to be divided into three equal angles using a compass and straightedge.


tangential triangle

en-noun

tangential triangle (plural tangential triangles)

A triangle formed of line segments tangential to the circumcircle of another triangle ABC at its vertices.


A polygon with 65537 sides and 65537 angles.


acutangled

12 An obliquangled triangle is either Obtuſangled or Acutangled.
The diviſion of an obliquangled triangle is taken from the ſpeciall differences of an oblique angle. For at the 15 e iij, we were taught that an oblique angle was either obtuſe or acute: Therefore an obliquangled triangle is an obtuſeangle, and an Acutangle.

1636, Peter Ramvs [i.e., Petrus Ramus], “Of Geometry, the ſeventh Booke, Of the compariſon of Triangles”, in William Bedvvell [i.e., William Bedwell], transl., Via Regia ad Geometriam: The VVay to Geometry, […] Thomas Cotes, […] Michael Sparke, page 111:

(geometry) Obsolete form of acute-angled.


obtusangled

(geometry) Obsolete form of obtuse-angled.


obliquangled

(geometry) Obsolete form of oblique-angled.


obliquangle

But if it be an obliquangle triangle, to note it with the letters BCD.

1618, John Napier, translated by Edward Wright, A description of the admirable table of logarithmes, London: […] Simon Waterson, page 3:

Notwithſtanding in obliquangle triangles, although the ſhankes are not the heights, the caulſe of the truth hereof is the ſame.

1636, Peter Ramvs [i.e., Petrus Ramus], “Of Geometry, the ſeventh Booke, Of the compariſon of Triangles”, in William Bedvvell [i.e., William Bedwell], transl., Via Regia ad Geometriam: The VVay to Geometry, […] Thomas Cotes, […] Michael Sparke, page 100:

IN an obliquangle Triangle, when the termes propounded are two ſides and one Angle , or two Angles and one ſide, and yet the terme required undiſcoverable by the two laſt premiſed Problemes, you are to convert ſuch a Triangle into two Rectangle Triangles, […]

1645, Edmund Wingate, “The uſe of the Rule of Proportion in Geometrie” (chapter 5), in Edmund Wingate, transl., The uſe of the Rule of Proportion: in Arithmetique and Geometrie, London: […] M. F. for P. Stephenss, Of Sphericall Obliquangle Triangles, page 59:

And here we may take in by the way, another kind of tetragonall Plane, very variable in reſpect of it's angles, but regular-like, (as I may term it) being equilaterall, though notequi-angular , called Rhombus, being the onely obliquangle equilaterall Parallelogram, and which therefore is a Quadrat, […]

1650, John Wyberd, Tactometria. Seu, Tetagmenometria. Or the Geometry of Regulars practically proposed; […] , […] Robert Leybourn, for Nathaniel Brooks, pages 102-103:

(geometry) Obsolete form of oblique angle.


(geometry) Synonym of enneacontagon: A polygon with 90 sides and 90 angles.


(geometry, rare) Synonym of chiliagon: A polygon with a thousand vertices and a thousand edges.


(geometry) Synonym of enneagon: A polygon with nine sides; a nonagon.


(geometry) Synonym of enneacontahexagon: A polygon with ninety six sides and ninety six angles.


(geometry, rare) Synonym of dihectagon: A polygon with two hundred sides and two hundred angles.


(geometry) Synonym of dodecagon: A polygon with twelve edges and twelve angles.


(geometry) Synonym of hexadecagon: A polygon with sixteen sides and sixteen angles.


(geometry) Synonym of decagon: A polygon with ten sides and ten angles.


(geometry) Synonym of heptadecagon: A polygon with seventeen sides and seventeen angles.


(geometry) Synonym of hendecagon: A polygon with eleven edges and eleven angles.


(geometry) Synonym of enneadecagon: A polygon with nineteen sides and nineteen angles.


(geometry, rare) Synonym of octadecagon: A polygon with 18 sides and 18 vertices.


(geometry) Synonym of icosidigon: A polygon with twenty two sides and twenty two angles.


(geometry) Synonym of quadrilateral: A polygon with four sides.


(geometry) Synonym of heptagon: A polygon with seven sides and seven angles.


(geometry) Synonym of icosagon: A polygon with twenty sides and twenty angles.


(geometry) Synonym of megagon: A polygon with one million sides.


(geometry) Synonym of icositetragon: A polygon with 24 sides and 24 angles.


(geometry) Synonym of hexacontagon: A 60-sided polygon.


(geometry) Synonym of hexagon: A polygon with six sides and six angles.


(geometry) Synonym of icosihenagon: A polygon with twenty-one edges and twenty-one angles.


(geometry) Synonym of myriagon: A polygon with 10,000 sides.


(geometry) Synonym of pentadecagon: A polygon with fifteen sides.


(geometry) Synonym of pentagon: A polygon with five sides and five angles.


(geometry) Synonym of octacontagon: A polygon with 80 sides and 80 angles.


(geometry) Synonym of tetracontagon: A 40-sided polygon.


(geometry) Synonym of tetracontadigon: A polygon with forty two sides and forty two angles.


(geometry) Synonym of tetracontakaihexagon: A polygon with forty six sides and forty six angles.


(geometry) Synonym of triacontadigon: A polygon with thirty-two sides and thirty-two angles.


(geometry) Synonym of icositrigon: A polygon with 23 sides and 23 angles.


(geometry) Synonym of tridecagon: A polygon having thirteen sides and thirteen angles.


(geometry) Synonym of triacontatetragon: A polygon with thirty four sides and thirty four angles.


(geometry) Synonym of heptacontagon: A polygon with seventy edges.


(geometry) Synonym of hectogon: A polygon having a hundred sides.


(geometry, also attributively) Synonym of octagon: A polygon with eight sides and eight angles.


(geometry) Synonym of triacontagon: A polygon with thirty sides.


(geometry) Synonym of tetradecagon: A polygon having fourteen sides and fourteen angles.


Cassini ellipse

Cassini ellipse (plural Cassini ellipses)


harmonic division

harmonic division (plural harmonic divisions)

(mathematics, geometry) The configuration of four ordered collinear points such that their cross-ratio is -1.