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 4 of 8: from “group” to “median”.
- group noun An effective divisor on a curve.
- group functor noun A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group.
- gyroparallelogram noun A hyperbolic quadrilateral whose two gyrodiagonals intersect at their gyromidpoints, analogous to a parallelogram in Euclidean space.
- halfspace noun Either of the two parts of a three-dimensional object cut by a two-dimensional plane
- handle noun The smooth, irreducible subcurve of a comb which connects to each of the other components in exactly one point.
- hecatonicosachoron noun A four-dimensional object analogous to a dodecahedron, constructed out of one hundred and twenty dodecahedra, arranged 4 to a vertex.
- hectogon noun A polygon having a hundred sides.
- Heegner point noun A point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane.
- height noun The minimum distance from a vertex of a triangle to (the extension of) the edge opposite, namely along a line perpendicular to the edge.
- hemiequilateral adj Describing the shape of a triangle formed by cutting an equilateral triangle in half through one of the apices
- hemisphere noun Any half-sphere, formed by a plane intersecting the center of a sphere. .
- heterocentric adj Having different or multiple centres.
- hexagonal adj Having six edges, or having a cross-section in the form of a hexagon.
- hexatetrahedron noun A cube truncated by two tetrahedra
- hexlet noun A chain of six spheres, each of which is tangent to both of its neighbours and also to three mutually tangent given spheres.
- holyhedron noun 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…
- homaloid noun An element of a homaloidal system, in particular the image of a hyperplane under a Cremona transformation.
- homaloidal adj flat; even; applied to surfaces and spaces in which the Euclidean definitions, axioms, and postulates respecting parallel straight lines…
- homocentric adj Having the same centre.
- homogeneous adj Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the…
- homogeneous coordinate noun Any one of a set of n + 1 coordinates which non-uniquely identify a point in an n-dimensional projective space; when such coordinates are…
- homographic adj Having the same invariants.
- homography noun An isomorphism between projective spaces that maps straight lines to straight lines.
- homology noun specifically, such relationship in the context of the geometry of perspective.
- homothetic adj for a geometric figure that is the image of another figure under an homothety.
- homothety noun An isotropic scaling transformation of an affine space with a single fixed point.
- honeycomb noun A space-filling packing of polytopes in three- or higher-dimensional space.
- hoof noun An ungula.
- horocyclic adj Relating to a set of points that are all equidistant (keeping other coordinates constant) from some constant point.
- hull noun The smallest set that possesses a particular property (such as convexity) and contains every point of A; slightly more formally, the…
- Hurwitz surface noun A compact Riemann surface with precisely 84(g − 1) automorphisms, where g is the genus of the surface. This number is maximal by virtue of…
- hyperbola noun A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone. The…
- hyperbole noun A hyperbola.
- hyperbolic adj Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.
- hyperbolic geometry noun A type of geometry that rejects the parallel postulate. Given a straight line L and a point p not on L, more than one straight line can be…
- hyperbolism noun A blow-up of a curve at a point.
- hypercube noun A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent…
- hypercusp noun A singularity of a curve of some multiplicity r whose tangent cone is a single line meeting the curve with order r+1.
- hypercycle noun A curve whose points have the same orthogonal distance from a given straight line.
- hyperellipse noun A superellipse: a curve in two dimensions of a certain type, a generalization of the ellipse.
- hyperflex noun A point of a curve where the tangent line has contact of order at least 4.
- hyperplane noun An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional…
- hypersphere noun The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more…
- hypertorus noun An N-dimensional equivalent of a torus, where N is a positive integer greater than 3.
- hypoellipse noun A superellipse with an exponent (shape parameter) smaller than that of the ellipse, i.e. less than two.
- hypotrochoid noun A geometric curve traced by a fixed point on the radius line outside one circle which rotates inside the perimeter of another circle.
- icosahedron noun A polyhedron with twenty faces.
- Iitaka dimension noun The Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space…
- imaginary geometry noun Absolute geometry, an axiomatised geometry in which the parallel postulate is absent and not replaced by an alternative, and of which…
- implicit function noun A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially…
- improper rotation noun An isometry in Euclidean space that is a combination of a rotation about an axis and a reflection in a plane perpendicular to that axis.
- incenter noun The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.
- incidence noun The falling of a point on a line, or a line on a plane.
- inclination noun The angle of intersection of a reference plane.
- indivisible noun An infinitely small quantity which is assumed to admit of no further division.
- inscribe verb To draw a circle, sphere, etc. inside a polygon, polyhedron, etc. and tangent to all its sides.
- insist verb To stand (on); to rest (upon); to lean (upon).
- interaxis noun A line from the center of a regular solid to the center of one of its edges.
- intercept noun The coordinate of the point at which a curve intersects an axis.
- intersection noun The point or set of points common to two geometrical objects (such as the point where two lines meet or the line where two planes…
- intersector noun That which intersects.
- inverse noun The result of a circle inversion; the set of all such points; the curve described by such a set.
- inversive geometry noun The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as…
- involute noun 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.
- irreducible adj Inexpressible as the union of two proper algebraic subvarieties.
- irregular adj Of a polygon, not regular; having sides that are not equal or angles that are not equal.
- irregular prism noun a prism whose cross section is an irregular polygon
- isocapacitary adj Having the same capacity; applied to the problem of finding an extremum for an integral over a space of a specified capacity.
- isodynamic adj In Euclidean geometry, being or relating to certain points associated with a triangle, with the properties that an inversion centered at…
- isogeny noun An epimorphism of group schemes that is surjective and has a finite kernel.
- isogonal adj Having equal angles.
- isogonic adj Having equal angles.
- isoperimetric adj Having the same perimeter; applied to the problem of finding a plane figure of the largest possible area whose boundary has a specified…
- isotomic adj Having equal but reflected cevians.
- Johnson solid noun Any of a class of convex polyhedra that have regular faces but are not uniform (that is, not Platonic solids, Archimedean solids, prisms…
- join noun The smallest linear space containing both of two given linear spaces.
- K-theory noun The study of rings R generated by the set of vector bundles over some topological space or scheme;
- Keller graph noun 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…
- Kepler solid noun Any of several nonconvex regular polyhedra with regular pentagrammatic faces or vertex figures and which can be obtained by stellation of…
- kissing number noun 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…
- kite noun A polygon resembling the shape of a traditional toy kite (sense 3): a quadrilateral having two pairs of edges of equal length, the edges of…
- lateral area noun The sum of the areas of the lateral (vertical) faces of a cylinder, cone, frustum, or the like.
- latus rectum noun The chord passing through a focus of a conic section, parallel to the directrix and terminated both ways by the curve. It is the parameter…
- leg noun One of the two sides of a right triangle that is not the hypotenuse.
- Lemoine hexagon noun 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…
- lemon noun The surface of revolution of a circular arc of angle less than 180° rotated about the straight line passing through the arc’s two endpoints.
- lens noun A convex shape bounded by two circular arcs, joined at their endpoints, the corresponding concave shape being a lune.
- lensoidal adj Of a lenticular shaped geometry.
- limaçon noun A plane curve with polar equation ρ=a+b, sin ,θ or ρ=a+b, cos ,θ, of which the cardioid is a special case.
- line noun An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness.
- line of centers noun A line joining centers of figures.
- line of striction noun The line on a skew surface that cuts each generator in that point of it that is nearest to the succeeding generator.
- lituus noun A curve with polar equation r²θ=a², where a is a constant.
- local adj Such that the following conditions are equivalent: (1) P holds for R (M); (2) P holds for the localization R_p (M_p) for all prime ideals p…
- lune noun A concave figure formed by the intersection of the arcs of two circles on a plane, or on a sphere the intersection between two great…
- lune of Hippocrates noun 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.
- major axis noun The longest diameter of an ellipse, running through the center and foci, with its ends being the widest points of the shape.
- Malfatti circle noun Any of the three circles inside a given triangle such that each circle is tangent to the others and to two sides of the triangle.
- Manhattan distance noun Synonym of taxicab distance (“the distance between two points on a grid, where the only path allowed is along horizontal and vertical…
- median noun A line segment joining the vertex of triangle to the midpoint of the opposing side.