This page gathers the 757 dictionary entries belonging to the domain “Geometry”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples. Page 1 of 8: from “-choron” to “center”.
- -choron suffix Used to form the names of 4-dimensional solids bounded by a certain number of cells/polyhedra (polychora).
- -gon suffix Forms the names of plane figures containing a given number of internal angles, and thus bounded by that number of line segments (polygons).
- 120-cell noun A four-dimensional polytope, analogous to a dodecahedron, whose 120 bounding facets are dodecahedra.
- 16-cell noun A four-dimensional polytope, analogous to an octahedron, whose sixteen bounding facets are tetrahedra.
- 24-cell noun A four-dimensional polytope whose twenty-four bounding facets are octahedra and which has no three-dimensional analogue.
- 4-cube noun A cube in four dimensions or four-dimensional space; a tesseract, 8-cell or octachoron; made of eight cubical cells or eight cubes.
- 8-cell noun A four-dimensional polytope, analogous to a cube, whose eight bounding facets are cubes; a tesseract.
- aberrancy noun The deviation of a curve from circular form.
- abscissa noun The first of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- absolute noun In a plane, the two imaginary circular points at infinity; in space of three dimensions, the imaginary circle at infinity.
- absolute geometry noun The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel…
- acatastatic adj Not catastatic.
- accidental adj Being a double point with two distinct tangent planes in 4-dimensional projective space.
- acnode noun An isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the…
- acutangular adj acute-angled.
- acute adj Less than 90 degrees.
- adjoint adj Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.
- affine adj Of or pertaining to a function expressible as f(⃑x)=A⃑x+⃑b (where A is a linear transformation and ⃑b is a constant), which, regarded as a…
- affine geometry noun The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.
- affine scheme noun An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of…
- affine transformation noun A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of…
- affine variety noun A set of points (in n-dimensional space) which satisfy a set of equations which have a polynomial of n variables on one side and a zero on…
- affinely independent adj Said of a set of points in an affine space: the property that the vectors issuing from an arbitrarily chosen point to the rest of the…
- affinity noun An automorphism of affine space.
- agonic adj Lacking an angle.
- algebraic analysis noun The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions…
- algebraic function noun Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a…
- algebraic variety noun The set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a…
- alternate verb To perform an alternation (removal of alternate vertices) on (a polytope or tessellation); to remove vertices (from a face or edge) as part…
- alternate angles noun the internal angles made by two (parallel) lines with a third, on opposite sides of it.
- alternation noun A type of partial truncation of a polygon, polyhedron or tiling in which alternate vertices are removed.
- altitude noun The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.
- anabelian adj Of or relating to anabelian geometry, a proposed theory describing the way the algebraic fundamental group G of an algebraic variety (or…
- anabelian geometry noun A theory which describes the way in which the algebraic fundamental group G of an algebraic variety (or some related geometric object) V…
- analogy noun The proportion or the equality of ratios.
- analytic geometry noun The subbranch of geometry that investigates geometrical figures via the mathematical properties of their representations in a coordinate…
- angle noun A figure formed by two rays which start from a common point (a plane angle) or by three planes that intersect (a solid angle).
- angle of torsion noun The indefinitely small angle between two consecutive osculating planes of a curve of double curvature.
- angular defect noun The amount by which the sum of the interior angles of a triangle is less than 180° (π radians); the amount by which the sum of the internal…
- anharmonic adj Describing the section of a line by four points, A, B, C, D, when their mutual distances are such that AB divided by CB is not equal to AD…
- anisotomic adj Not isotomic
- annulus noun The region in a plane between two concentric circles of different radii.
- anticomplementary adj antimedial
- antimedial adj Being a triangle formed by three lines parallel to the sides of an original triangle ABC: the parallel to AB through C, the parallel to AC…
- antinormal noun A normal that points opposite to convention. For example, in solid geometry it is conventional for normals to point outwards, so an…
- antiparallel noun A line that forms equal angles with two other lines, but in opposite directions.
- antipole noun A position directly opposite (possibly also used figuratively).
- apeirogon noun A type of generalised polygon with a countably infinite number of sides and vertices;
- apex noun The highest point in a plane or solid figure, relative to a base line or plane.
- apolar adj Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.
- Apollonian circle noun Any circle in two families of circles such that every circle in the first family intersects every circle in the second family orthogonally…
- apothem noun The perpendicular distance from the center of a circle to a chord of the same circle.
- apotome noun The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the…
- apple noun The surface of revolution of a circular arc of an angle greater than 180° rotated about the straight line passing through the arc's two…
- arbelos noun A plane region bounded by a semicircle of diameter 1, connected to semicircles of diameters r and (1 − r), all oriented the same way and…
- arc noun A continuous part of the circumference of a circle (circular arc) or of another curve.
- arch noun An arc; a part of a curve.
- Archimedean solid noun Any of a class of convex semiregular polyhedra, composed of two or more types of regular polygon meeting in identical vertices.
- Aronhold set noun One of the 288 sets of seven of the 28 bitangents of a quartic curve corresponding to the seven odd theta characteristics of a normal set.
- augmented sphenocorona noun A polyhedron, one of the Johnson solids, whose faces are composed of 16 equilateral triangles and one square.
- axis noun An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry).
- axle noun An axis.
- B-sheaf noun 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…
- barycenter noun The centroid, the geometric center of a plane figure
- base noun The lowest side of a triangle or other polygon, or the lowest face of a cone, pyramid or other polyhedron laid flat.
- bicapped adj Having a cap (in the shape of a pyramid) at each end
- bicircular adj Having nodes at the two circular points at infinity.
- bicone noun The three-dimensional shape swept by revolving an isosceles triangle around its edge of unequal length, or by joining two identical right…
- bielliptic adj Being a branched double cover of an elliptic curve.
- birational geometry noun A field of algebraic geometry in which the aim is to determine under what conditions two algebraic varieties are isomorphic outside…
- biregular adj Being a regular map with regular inverse.
- biscribed adj Both circumscribed and inscribed, i.e. having vertices that lie on a curve and sides that are tangent to the curve.
- bisect noun A bisector, which divides into two equal parts.
- bisector noun A line or curve that bisects or divides a line segment, angle, or other figure into two equal parts.
- bispherical adj Composed of two spheres.
- bitangential adj Meeting a curve at the tangency points of its bitangents.
- blockwise adj Allowing movement vertically or horizontally only, as if navigating the edges of a grid pattern.
- body noun A three-dimensional object, such as a cube or cone.
- bounding adj Containing all points of a given set within it.
- box noun A rectangular object in any number of dimensions.
- boxcar function noun Any function whose value is zero except for a finite part of its argument for which it has a constant non-zero value.
- branch noun One of the portions of a curve that extends outwards to an indefinitely great distance.
- Bravais lattice noun An infinite array of discrete points generated by a set of discrete translation operations mathbf R=n_1 mathbf a₁+n_2 mathbf a₂+n_3 mathbf…
- Brocard circle noun A circle that passes through the circumcenter and symmedian of a given triangle, and is centered at the midpoint of the line segment…
- Brocard point noun The point inside a triangle at the intersection of the lines through each vertex such that the angle between the line and the side of the…
- Brocard triangle noun The triangle formed by joining the points of intersection of the lines from each vertex of a triangle to its Brocard points.
- Calabi-Yau manifold noun A kind of manifold having properties, such as Ricci flatness, that yield applications in theoretical physics.
- cantellation noun An operation in any dimension that cuts a regular polytope at its edges and its vertices, creating a new facet in place of each edge and…
- cap noun A portion of a spherical or other convex surface.
- cardioid noun An epicycloid with exactly one cusp; the plane curve with polar equation ρ=1+ cos ,θ - approximately heart-shaped
- Cartesian coordinate noun The coordinates of a point measured from an origin along a horizontal axis from left to right (the x-axis) and along a vertical axis from…
- Cartesian coordinates noun The coordinates of a point measured as its perpendicular distance to the right of a vertical axis (the y-axis) and its perpendicular…
- Cartesian equation noun An equation that describes a line or plane in terms of the relationship between the coordinates on the axes involved.
- Cartesian product noun An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent…
- Cassini oval noun A plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant…
- catenarian adj Shaped like a catenary; following the curve made by a chain or rope when suspended from both ends.
- catenary noun The curve described by a flexible chain or a rope if it is supported at each end and is acted upon by no other forces than a uniform…
- cathetus noun A line perpendicular to a surface (or line); in particular, either of the sides of a right triangle other than its hypotenuse.
- cell noun A three-dimensional facet of a polytope.
- center noun The point on a line that is midway between the ends.