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 3 of 8: from “disk” to “groin”.
- disk noun A two-dimensional geometric region, the set of points bounded by a circle.
- disphenoid noun A non-regular tetrahedron whose four faces are congruent acute-angled triangles.
- distinguished open set noun A particularly basic kind of set, generalizing the notion of the complement of a hypersurface, originating in the study of algebraic…
- divisor noun An element of the free abelian group on the points of the space.
- dodecahedron noun A polyhedron with twelve faces; the regular dodecahedron has regular pentagons as faces and is one of the Platonic solids.
- domino noun A polyomino made up of two squares.
- Donaldson-Thomas invariant noun Given a compact moduli space of sheaves on a Calabi-Yau threefold, its Donaldson-Thomas invariant is the virtual number of its points…
- double point noun A point on a curve at which there are two tangents (because it touches itself, or has a cusp).
- double rotation noun Two rotations (of an object with four or more dimensions) that happen simultaneously along two different two-dimensional planes without…
- dual noun Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
- dual polyhedron noun Either of a pair of polyhedra in which the faces of one are equivalent to the vertices of the other.
- duocylinder noun A geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks, and analogous to a cylinder in…
- dyakis dodecahedron noun A variant of the deltoidal icositetrahedron with pyritohedral symmetry, transforming the kite faces into chiral quadrilaterals.
- eccentric noun A circle not having the same centre as another.
- eccentricity noun The ratio, constant for any particular conic section, of the distance of a point from the focus to its distance from the directrix.
- ecliptic noun A great circle drawn on a terrestrial globe, used for illustrating and solving astronomical problems.
- edge noun A one-dimensional face of a polytope. In particular, the joining line between two vertices of a polygon; the place where two faces of a…
- effective adj Having no negative coefficients.
- elation noun A collineation that fixes all points on a line (called its axis) and all lines though a point on the axis (called its center).
- ellipse noun A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the…
- ellipsis noun An ellipse.
- ellipsoid noun A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian…
- elliptic adj Of or pertaining to an ellipse.
- elliptic curve noun The algebraic set of an equation which equates the square of one variable to a reduced cubic polynomial in another variable, over some…
- elongated adj Of a polyhedron, having been modified by placing a prism in the middle of the polyhedron.
- enclosing adj Of a region, containing all points of a given set within its bounds.
- envelope noun A mathematical curve, surface, or higher-dimensional object that is the tangent to a given family of lines, curves, surfaces, or…
- epicycle noun Any circle whose circumference rolls around that of another circle, thus creating a hypocycloid or epicycloid.
- epicycloid noun The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.
- equal detour point noun A triangle center characterized by the property that, if one travels from any vertex of the triangle to another by taking a detour through…
- equiangular adj Of a polygon, having all interior angles equal. This is not necessarily a regular polygon, since that would also be equilateral; a…
- equianharmonic noun A set of four points whose cross ratio (or anharmonic ratio) is a cube root of 1.
- equilateral adj Having all the sides equal.
- equiregular adj Having both all sides equal length and all angles equal.
- equivalence noun A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this…
- equivalent adj Equal in measure but not admitting of superposition; applied to magnitudes.
- escribe verb 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.
- essential adj Such that each complementary region is irreducible, the boundary of each complementary region is incompressible by disks and monogons in…
- Euclidean adj Adhering to the principles of traditional geometry, in which parallel lines are equidistant.
- Euclidean distance noun The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding…
- Euler angle noun Any one of three angles which together describe the orientation of a rigid body with respect to a fixed three-dimensional coordinate…
- Euler line noun A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an…
- evectant noun A contravariant constructed from an invariant by acting on it with a differential operator called an evector.
- evolute noun A curve comprising the centres of curvature of another curve.
- evolution noun The opening out of a curve; now more generally, the gradual transformation of a curve by a change of the conditions generating it.
- excentral adj Relating to the excentre.
- exceptional adj Corresponding to something of lower dimension under a birational correspondence.
- excess noun Spherical excess, the amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is…
- excircle noun An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the…
- expansion noun Stretching of geometric objects with flat sides.
- face noun Any of the flat bounding surfaces of a polyhedron; more generally, any of the bounding pieces of a polytope of any dimension.
- facultative adj At which a given function is positive.
- Fano plane noun The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3…
- Fermat point noun A point such that the sum of the three distances from each of the three vertices of a given triangle to that point is the smallest…
- Feuerbach point noun A kind of triangle center, defined as the point at which the incircle and nine-point circle of the triangle are internally tangent to each…
- Fibonacci spiral noun An approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in a Fibonacci tiling; a…
- finite geometry noun Any geometric system that has only a finite number of points.
- flag noun A sequence of faces of a given polytope, one of each dimension up to that of the polytope (formally, though in practice not always…
- flat noun A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
- flex noun A point of inflection.
- flexagon noun A flat model made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.
- focal noun One of two lines perpendicular to the axis of a cone such that the cosine of the angle between the line and the axis is equal to the ratio…
- focaloid noun A shell bounded by two concentric, confocal ellipses (in two dimensions) or ellipsoids (in three dimensions).
- focus noun A point of a conic at which rays reflected from a curve or surface converge.
- foliate noun A logocyclic curve.
- folium noun A curve of the third order, consisting of two infinite branches having a common asymptote. The curve has a double point, and a leaf-shaped…
- foot noun The point of intersection of one line with another that is perpendicular to it.
- Ford circle noun Any one of a class of circles with centre at (p/q, 1/(2q²)) and radius 1/(2q²), where p/q is an irreducible fraction (i.e., p and q are…
- form noun A quantic.
- four-dimensional adj Having four dimensions; being measurable along four mutually perpendicular axes.
- fourgon noun A polygon with four sides; a quadrilateral.
- Fourier-Mukai transform noun A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform…
- fourth dimension noun The fourth coordinate indicating a position along the fourth axis.
- Frobenioid noun A category with some extra structure that generalizes the theory of line bundles on models of finite extensions of global fields.
- full circle noun An arc of 360 degrees.
- funicular adj Synonym of catenary.
- Gauss map noun A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal…
- Gauss-Codazzi equation noun Any of a group of fundamental formulas in Riemannian and pseudo-Riemannian geometry that link together the induced metric and second…
- generant adj acting as a generant.
- generation noun The formation or production of any geometrical magnitude, as a line, a surface, a solid, by the motion, in accordance with a mathematical…
- generator noun One of the lines of a ruled surface; more generally, an element of some family of linear spaces.
- generic adj Of a point, having coordinates that are algebraically independent over the base field.
- generic property noun A property that is true in some dense open subset of a given set.
- genus noun A natural number representing any of several related measures of the complexity of a given manifold or graph.
- geodesic noun The shortest curve between two points on a specific surface.
- geometric analysis noun A branch of mathematics in which techniques from differential geometry are used in the analysis and solution of partial differential…
- geometry noun A mathematical object comprising representations of a space and of its spatial relationships.
- Gergonne point noun A certain triangle center. Given a triangle ∆ABC and its Gergonne triangle (with the touchpoint opposite A denoted by T_A, etc.), the…
- glome noun 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…
- gnomon noun A plane figure formed by removing a parallelogram from a corner of a larger parallelogram.
- golden ratio noun The irrational number (approximately 1.618), usually denoted by the Greek letter φ (phi), which is equal to the sum of its own reciprocal…
- golden section noun 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…
- golygon noun A serial isogon of 90 degrees; any polygon with all right angles, whose sides are consecutive integer lengths.
- gömböc noun A convex shape which, if made of a uniformly dense material, has one stable equilibrium orientation and one unstable equilibrium…
- grade noun In a linear system of divisors on an n-dimensional variety, the number of free intersection points of n generic divisors.
- great circle noun A circle defined as the intersection of the surface of a sphere and a plane which passes through the centre of the sphere.
- great icosihemidodecahedron noun A polyhedron having 26 faces, 30 vertices, 60 edges, six self-intersected faces, and six nonconvex faces.
- great rhombicuboctahedron noun An Archimedean solid that is isogonal and has twenty-six regular faces (twelve square, eight hexagonal and six octagonal).
- gree noun A degree.
- groin noun The surface formed by two such vaults.