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 2 of 8: from “centerpoint” to “disdyakis triacontahedron”.
- centerpoint noun A generalization of the median to data in higher-dimensional Euclidean space.
- centroid noun The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly…
- Chern class noun Any of a group of characteristic classes associated with complex vector bundles, with applications in physics, string theory, etc.
- chiral adj that exhibits chirality; as in the left-handed and right-handed versions of a helix, or a molecule with L- and D- stereoisomers.
- chord noun A line segment between two points of a curve.
- circle noun A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given…
- circle inversion noun A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the…
- circle of Apollonius noun The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\frac).
- circumcenter noun The center of a circumcircle (the circle that passes through every vertex of a given triangle or other cyclic polygon).
- circumference noun The line that bounds a circle or other two-dimensional figure.
- circumscribe verb To draw the smallest circle or higher-dimensional sphere that has (a polyhedron, polygon, etc.) in its interior.
- cissoid noun Any of a family of curves defined as the locus of a point, P, on a line from a given fixed point and intersecting two given curves, C₁ and…
- Clawson point noun A point in a triangle defined by the trilinear coordinates tan α : tan β : tan γ, where α, β, γ are the interior angles at the triangle…
- cleaver noun A line segment that bisects the perimeter of a triangle and has one endpoint at the midpoint of one of the triangle's three sides.
- cline noun A generalized circle.
- closed adj Lacking endpoints. For parametric curves, with the same image for the ends of the domain.
- coaxial adj Having a common central axis
- coincidence noun A fixed point of a correspondence; a point of a variety corresponding to itself under a correspondence.
- collinear adj Lying on the same straight line.
- comb noun A connected and reduced curve with irreducible components consisting of a smooth subcurve (called the handle) and one or more additional…
- combinatorial geometry noun The field of mathematics which examines extremal problems of a combinatorial nature expressed geometrically.
- compass error noun The combination of variation and deviation which is the horizontal angle between the direction indicated by a magnetic compass and true…
- complement noun An angle which, together with a given angle, makes a right angle.
- complex adj A curve, polygon or other figure that crosses or intersects itself.
- complex projective line noun A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective…
- computational geometry noun A field of study, within computer science, devoted to algorithms that solve problems formulated in geometric terms.
- concave adj Not convex; having at least one internal angle greater than 180 degrees.
- concentric adj Having a common center.
- conchoid noun Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and…
- concurrent adj Meeting in one point.
- cone noun A surface of revolution formed by rotating a segment of a line around another line that intersects the first line.
- confluent adj Exactly the same size as another triangle.
- conformal geometry noun The study of conformal (angle-preserving) transformations on a space;
- congruence noun The quality of being isometric — roughly, the same measure and shape.
- conic noun A conic section.
- conic section noun Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola, and hyperbola.
- conical adj Of or relating to a cone or cones.
- conical surface noun Synonym of cone (“a surface of revolution formed by rotating a segment of a line around another line that intersects the first line or a…
- conjugate axis noun Either of two axes in a conic section, such that each is parallel to the tangent at the extremity of the other.
- conoid noun A Catalan surface all of whose rulings intersect some fixed line
- construct verb To draw (a geometric figure) by following precise specifications and using geometric tools and techniques.
- constructible adj That can be constructed in a plane using only a pair of compasses and a straightedge.
- construction noun A geometric figure of arcs and line segments that is drawable with a straightedge and compass.
- contact number noun Synonym of kissing number.
- contingence noun Contact; touching.
- convex adj having no internal angles greater than 180 degrees.
- coordinate system noun A method of representing the position of any individual point in a space of given dimensionality as a tuple of numerical coordinates.
- coöriginal adj Originating from the same point in space.
- coplanar adj Within the same plane.
- coplanarity noun The state or characteristic of being within the same plane.
- coreset noun A small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets…
- coterminal adj Differing only by a whole number of complete circles.
- Cox ring noun A sort of universal homogeneous coordinate ring for a projective variety, and (roughly speaking) a direct sum of the spaces of sections of…
- Coxeter group noun Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but…
- Coxeter-Dynkin diagram noun A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting…
- cross-polytope noun A polytope that is the convex hull of points, two on each Cartesian axis of a Euclidean space, that are equidistant from the origin; an…
- cross-ratio noun A special number associated with an ordered quadruple of collinear points, particularly points on a projective line, and preserved by the…
- crown noun The area enclosed between two concentric perimeters.
- cube noun A regular polyhedron having six identical square faces.
- cubic adj Used in the names of units of volume formed by multiplying a unit of length by itself twice.
- cubicuboctahedron noun Either of two star polyhedra whose square faces are parallel to a square and whose triangular faces are parallel to those of an octahedron
- cubinder noun A cubical cylinder (four-dimensional analog of a cylinder)
- cubo-cubic adj Being a Cremona transformation such that the homaloids of the transformation and its inverse all have degree 3.
- cuboctahedron noun An Archimedean solid that has fourteen faces (eight triangular and six square) and is both isogonal and isotoxal.
- cuboid noun A hexahedron.
- cuboidal adj Of, pertaining to, or having the shape of a cuboid.
- cupola noun A solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles…
- curve noun A continuous map from a one-dimensional space to a multidimensional space.
- curvilinear adj Formed by curved lines.
- cusp noun A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.
- cyclic adj Able to be inscribed in a circle.
- cycloid noun The locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line.
- cylinder noun A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.
- cylindricity noun The quality of being cylindrical.
- cylindroid noun A cylinder with elliptical cross-section.
- dart noun A concave quadrilateral similar in shape to a chevron or arrowhead.
- de Longchamps point noun A triangle center defined as the reflection of the orthocenter of the triangle about the circumcenter.
- decagram noun A ten-pointed star polygon.
- deficiency noun The amount by which the number of double points on a curve is short of the maximum for curves of the same degree.
- degree noun A unit of measurement of angle equal to ¹⁄₃₆₀ of a circle's circumference.
- Delaunay triangulation noun For a given set P of discrete points in a plane: a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle…
- deltoid noun A kite (quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end).
- deltoidal hexecontahedron noun A Catalan solid with 60 kite faces, 120 edges and 62 vertices, being the dual of the rhombicosidodecahedron.
- deltoidal icositetrahedron noun A convex polyhedron that has 24 congruent kite-shaped faces and 48 edges and is a Catalan solid, being the dual polyhedron of the…
- Desargues configuration noun A configuration of ten points and ten lines, with three points per line and three lines per point, whose existence is proven by Desargues'…
- developable noun A developable surface.
- developable surface noun A surface (in more than two dimensions, a plane is trivially developable) that can be flattened into a plane without distortion.
- dextrorse adj Having a negative torsion.
- diagonal adj Joining two nonadjacent vertices (of a polygon or polyhedron).
- diameter noun Any straight line between two points on the circumference of a circle that passes through the center of the circle; a chord that passes…
- diamond noun A rhombus, especially when oriented so that its longer axis is vertical.
- difference quotient noun The slope of the secant line passing through the points (a,,f(a)) and (a+h,,f(a+h)). As the horizontal distance h>0 between the points…
- differential geometry noun The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and…
- digit noun Synonym of degree: ¹⁄₃₆₀ of a circle.
- digon noun A polygon having two edges and two vertices.
- dimension noun The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent…
- directrix noun 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…
- dirigent noun The line of motion of a describent line or surface that in so moving defines a plane or solid figure; a directrix.
- discriminant noun The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pⁿ⁻¹…
- disdyakis triacontahedron noun A Catalan solid with 120 scalene triangle faces, 180 edges and 62 vertices, being the dual of the truncated icosidodecahedron.