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human or social attributes of place identity and sense of place than on geometry. A populated place is called a settlement. A locality, settlement, or populated

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It

In classical geometry, a radius (pl.: radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical

In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical

In geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the

In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {1}. In Euclidean geometry a monogon

In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular

In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular

In geometry, a hypotenuse is the side of a right triangle opposite to the right angle. It is the longest side of any such triangle; the two other shorter

In geometry, a kisrhombille is a uniform tiling of rhombic faces, divided by central points into four triangles. Examples: 3-6 kisrhombille – Euclidean

In geometry, a rotunda is any member of a family of dihedral-symmetric polyhedra. They are similar to a cupola but instead of alternating squares and

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling

In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides

Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled

In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral

In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation, from Latin

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself

In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold M {\displaystyle M} is called tame if it is

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general n-polytope is sliced off. Take some corner or vertex

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed. It is

In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different

In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally

In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed. It is part of a dimensionally

In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 tetrahedron cells, 8064

In differential geometry and complex geometry, a complex manifold is a manifold with a complex structure, that is an atlas of charts to the open unit

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object. For example, a cube has six faces in

In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given

In the mathematical field of differential geometry, a Kenmotsu manifold is an almost-contact manifold endowed with a certain kind of Riemannian metric

In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is

In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.

In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and

In geometry, a frustum (Latin for 'morsel'); (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two

In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both planes

In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10

In geometry, a pentagonal polytope is a regular polytope in n dimensions constructed from the Hn Coxeter group. The family was named by H. S. M. Coxeter

In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract

In geometry, a shape is said to be anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that

In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016

In geometry, a 9-simplex is a self-dual regular 9-polytope. It has 10 vertices, 45 edges, 120 triangle faces, 210 tetrahedral cells, 252 5-cell 4-faces

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube

In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning

In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cell

In geometry, a bigon, digon, or a 2-gon, is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because

In geometry, a 10-cube is a ten-dimensional hypercube. It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces

In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes.

In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the En Coxeter group, and having only regular polytope facets.

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It

In geometry, a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron;

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices. A

In geometry, a bicupola is a solid formed by connecting two cupolae on their bases. Here, two classes of bicupola are included because each cupola (bicupola

In geometry, a 10-simplex is a self-dual regular 10-polytope. It has 11 vertices, 55 edges, 165 triangle faces, 330 tetrahedral cells, 462 5-cell 4-faces

In geometry, a triangular prism or trigonal prism is a prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular

In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar

In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron

In differential geometry a Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this

organized under the auspices of the newly formed Society for Computational Geometry. A 2010 assessment of conference quality by the Australian Research Council

In geometry, a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex. It has variously

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the

In geometry, a tile substitution is a method for constructing highly ordered tilings. Most importantly, some tile substitutions generate aperiodic tilings

In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name hendecagram combines a Greek numeral prefix

In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell

In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every

In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not

In differential geometry, a hypercomplex manifold is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such

In geometry, a myriagon or 10000-gon is a polygon with 10000 sides. Several philosophers have used the regular myriagon to illustrate issues regarding

as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it. In differential geometry, a geodesic is a

In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle') is any five-sided polygon or 5-gon. The sum of the internal angles

In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting

In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον  'arc') or edge-transitive if its symmetries

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to

In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes

In geometry, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction as C at these points.

In geometry, a birotunda is any member of a family of dihedral-symmetric polyhedra, formed from two rotunda adjoined through the largest face. They are

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron.

Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component. As a consequence

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and

In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and

Look up trapezoid in Wiktionary, the free dictionary. In geometry, a trapezoid (/ˈtræpəzɔɪd/) in North American English, or trapezium (/trəˈpiːziəm/)

that the image of every line g is a line parallel to g. In projective geometry, a homothetic transformation is a similarity transformation (i.e., fixes

In geometry, a 65537-gon is a polygon with 65,537 (216 + 1) sides. The sum of the interior angles of any non–self-intersecting 65537-gon is 11796300°

In geometry, a 6-demicube, demihexeract or hemihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed

In geometry, a square pyramid is a pyramid with a square base and four triangles, having a total of five faces. If the apex of the pyramid is directly

In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using septa- (an elision

In differential geometry, a field in mathematics, Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms,

In geometry, a square pyramid is a pyramid with a square base and four triangles, having a total of five faces. If the apex of the pyramid is directly

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of

In geometry, a dodecagram (from Greek δώδεκα (dṓdeka) 'twelve' and γραμμῆς (grammēs) 'line') is a star polygon or compound with 12 vertices. There is

Various visualizations of the icosahedron edit In geometry, a Schlegel diagram is a projection of a polytope from R d {\textstyle \mathbb {R} ^{d}} into

In geometry, a tessellation of dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices

In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees. The regular triacontagon

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of

In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire

In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes

In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the

In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become

In Euclidean geometry, a harmonic quadrilateral is a quadrilateral whose four vertices lie on a circle, and whose pairs of opposite edges have equal products

In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron

In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called

In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from

In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces

In geometry, a 257-gon is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°. The area of a regular

In geometry, a triakis tetrahedron (or tristetrahedron, or kistetrahedron) is a solid constructed by attaching four triangular pyramids onto the triangular

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the

is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. A regular tetradecagon has Schläfli symbol {14} and can be constructed

In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional

In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon. A regular tridecagon is represented by Schläfli symbol {13}. The measure

Look up tesseract in Wiktionary, the free dictionary. In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional

In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment

In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from

In geometry, a chiliagon (/ˈkɪliəɡɒn/) or 1,000-gon is a polygon with 1,000 sides. Philosophers commonly refer to chiliagons to illustrate ideas about

In differential geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming

In algebraic geometry, a generic point P of an algebraic variety X is a point in a general position, at which all generic properties are true, a generic

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface)

In geometry, a deltoidal hexecontahedron (also sometimes called a trapezoidal hexecontahedron, a strombic hexecontahedron, or a tetragonal hexacontahedron)

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic

In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called

In geometry, a regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Regular octahedra occur

In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean

In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube) is a Catalan solid. Its dual is the truncated

See also Line (geometry) A lineament is a linear feature in a landscape which is an expression of an underlying geological structure such as a fault.

In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon. A regular pentadecagon is represented by Schläfli symbol {15}. A

In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography

In geometry, a circular segment or disk segment (symbol: ⌓) is a region of a disk which is "cut off" from the rest of the disk by a straight line. The

In geometry, a centre (Commonwealth English) or center (American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point

In algebraic geometry, a Newton–Okounkov body, also called an Okounkov body, is a convex body in Euclidean space associated to a divisor (or more generally

In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated

In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to

In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron) or d48, is

In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric

In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but

In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making

In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any

In geometry, a pentagonal trapezohedron is the third in the infinite family of trapezohedra, face-transitive polyhedra. Its dual polyhedron is the pentagonal

\left[{\begin{smallmatrix}0.5&0\\0&0.5\end{smallmatrix}}\right]} . In geometry, a diagonal matrix may be used as a scaling matrix, since matrix multiplication

or Johann Bolyai, was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry

In geometry, a golden rectangle is a rectangle with side lengths in golden ratio 1 + 5 2 : 1 , {\displaystyle {\tfrac {1+{\sqrt {5}}}{2}}:1,} or ⁠ φ :

In geometry, a conical surface is an unbounded surface in three-dimensional space formed from the union of infinite lines that pass through a fixed point

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) {\displaystyle

In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent

Join (sigma algebra), a refinement of sigma algebras Join (algebraic geometry), a union of lines between two varieties In computing: Join (relational algebra)

σφαῖρα, sphaîra) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from

In mathematics, and more specifically in differential geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely

Mathematically, clipping can be described using the terminology of constructive geometry. A rendering algorithm only draws pixels in the intersection between the

Wikimedia Commons has media related to Decahedra. In geometry, a decahedron is a polyhedron with ten faces. There are 32300 topologically distinct decahedra

In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed

In algebraic geometry, a lemniscate (/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt, -kɪt/) is any of several figure-eight or ∞-shaped curves. The word comes from the

In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates)

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning)

In geometry, a set S {\displaystyle S} in the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is called a star domain (or star-convex set, star-shaped

In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than

In geometry, a hyperrectangle (also called a box, hyperbox, k {\displaystyle k} -cell or orthotope), is the generalization of a rectangle (a plane figure)

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the

In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and

In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g − 1)

In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is

In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices. The word circumsphere

In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes

In geometry, a flat is an affine subspace, i.e. a subset of an affine space that is itself an affine space. Particularly, in the case the parent space

Euclidean geometry Nikolai Ivanovich Lobachevsky (1792–1856) – hyperbolic geometry, a non-Euclidean geometry Michel Chasles (1793–1880) – projective geometry

written as: x 2 + 2 a y = 0. {\displaystyle x^{2}+2ay=0.} In projective geometry, a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity

In classical algebraic geometry, a tacnode (also called a point of osculation or double cusp) is a kind of singular point of a curve. It is defined as

In geometry, a skew polygon is a closed polygonal chain in Euclidean space. It is a figure similar to a polygon except its vertices are not all coplanar

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting

In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain ⁠ P {\displaystyle P} ⁠ is a curve specified by

In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured

covered by a dome. Rotunda or The Rotunda may also refer to: Rotunda (geometry), a family of dihedral-symmetric polyhedra with alternating pentagons and

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section

In geometry, a Reinhardt polygon is an equilateral polygon inscribed in a Reuleaux polygon. As in the regular polygons, each vertex of a Reinhardt polygon

In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron or omnitruncated

In Euclidean geometry, a tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within

dictionary. In painting, photography, graphical perspective and descriptive geometry, a picture plane is an image plane located between the "eye point" (or oculus)

In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G

In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon. A regular heptadecagon is represented by the Schläfli symbol {17}. As

areas of formal languages, programming language semantics, and discrete geometry. A 2006 citation for an honorary doctorate (Ph.D.) called Nivat one of the

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one

geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional manifolds. Both contact and symplectic

of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is

In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb

In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution

the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles

definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in

In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface

In differential geometry, a fibered manifold is surjective submersion of smooth manifolds Y → X. Locally trivial fibered manifolds are fiber bundles.

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)

In geometry, a rhombic enneacontahedron (plural: rhombic enneacontahedra) is a polyhedron composed of 90 rhombic faces; with three, five, or six rhombi

In geometry, a spherical shell (a ball shell) is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric

In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R,

In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular

In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves

In geometry, a pentagonal pyramid is a pyramid with a pentagon base and five triangular faces, having a total of six faces. It is categorized as a Johnson

In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent

In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle

In geometry, a disphenoid (from Greek sphenoeides 'wedgelike') is a tetrahedron whose four faces are congruent acute-angled triangles. It can also be

In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped

In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs")

and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions

Twentieth Century"; "Wroclaw: Yesterday, Today, Tomorrow"; "The Art of Geometry: A Gallery of Polish Geometrical and Constructivist Art". Wroclaw Museums

rocket (such as the Saturn V), which is shaped like a truncated cone (in geometry, a kind of frustum). Payload fairings have usually been either burned up

In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed

In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged

functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function

these notations for the sides: AB, BC, CD, DA. But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, that is, AB = CD and

necessarily orthogonal to each other. See tensor. Affine differential geometry, a geometry that studies differential invariants under the action of the

In geometry, a hexecontahedron (or hexacontahedron) is a polyhedron with 60 faces. There are many symmetric forms, and the ones with highest symmetry

In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space

In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical

In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M {\displaystyle M} , equipped with a closed nondegenerate

anatomical directions describing relationships in an animal body In geometry: a geometric term of location an axis of rotation In chemistry, referring

In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle

mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any

In geometry, a pentahedron (pl.: pentahedra) is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides and there

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and

In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra

equations in a vacuum with vanishing cosmological constant. In Lorentzian geometry, a number of Ricci-flat metrics are known from works of Karl Schwarzschild

In geometry, a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron, kisrhombic triacontahedron or d120 is a Catalan solid with 120 faces

In geometry, a bitruncation is an operation on regular polytopes. The original edges are lost completely and the original faces remain as smaller copies

In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and

In geometry, a bipyramid, dipyramid, or double pyramid is a polyhedron formed by fusing two pyramids together base-to-base. The polygonal base of each

In differential geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex

In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared

In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: A x 4

In plane geometry, a lune (from Latin luna 'moon') is the concave-convex region bounded by two circular arcs. It has one boundary portion for which the

In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of

In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of

In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only

In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of

In geometry, a curve of pursuit is a curve constructed by analogy to having a point or points representing pursuers and pursuees; the curve of pursuit

In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six triangular faces that meet at a point (the apex). Like

hyperbola, a type of smooth curve lying in a plane in mathematics Hyperbolic geometry, a non-Euclidean geometry Hyperbolic functions, analogues of ordinary trigonometric

In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend

In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning

In geometry, a spirangle is a spiral polygonal chain. Spirangles are similar to spirals in that they expand from a center point as they grow larger, but

In mathematics, particularly differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a

In projective geometry, a dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There

In Euclidean plane geometry, a pseudotriangle (pseudo-triangle) is the simply connected subset of the plane that lies between any three mutually tangent

In geometry, a Cairo pentagonal tiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations

to: Kite (bird), the common name for a number of birds of prey Kite (geometry), a quadrilateral with reflection symmetry across a diagonal Kite (.hack)

In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the concept of caustics in geometric

In geometry, a tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms

In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as

In geometry, a hippopede (from Ancient Greek ἱπποπέδη (hippopédē) 'horse fetter') is a plane curve determined by an equation of the form ( x 2 + y 2 )

In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting

In geometry, a polygon (/ˈpɒlɪɡɒn/) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal

In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution

In differential geometry, a G-structure on an n-manifold M, for a given structure group G, is a principal G-subbundle of the tangent frame bundle FM (or

In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex. There are 5 degrees

In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space in which every point

In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight

In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are

In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely

In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube. There are 6 unique cantellation

In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex. There are three unique

In geometry, a hemi-dodecahedron is an abstract, regular polyhedron, containing half the faces of a regular dodecahedron. It can be realized as a projective

In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertices all lie on a single circle, making

In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex. There are unique 3 degrees

In geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of

In abstract geometry, a hemicube is an abstract, regular polyhedron,[citation needed] produced by cutting a cube in half with a plane that passes through

real projective plane. The difference is that as a model of elliptic geometry a metric is introduced permitting the measurement of lengths and angles

In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of

being null set, meaning "with probability 0". In topology and algebraic geometry, a generic property is one that holds on a dense open set, or more generally

In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties

In geometry, a trochoid (from Greek trochos 'wheel') is a roulette curve formed by a circle rolling along a line. It is the curve traced out by a point

In differential geometry, a saddle tower is a minimal surface family generalizing the singly periodic Scherk's second surface so that it has N-fold (N > 2)

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows

Wiktionary, the free dictionary. Hemisphere may refer to: Hemisphere (geometry), a half of a sphere A hemisphere of Earth Northern Hemisphere Southern Hemisphere

Central's The Colbert Report. Carroll is the author of Spacetime And Geometry, a graduate-level textbook in general relativity, and has also recorded

In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex. There are three unique

In five-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical

In five-dimensional geometry, a truncated 5-simplex is a convex uniform 5-polytope, being a truncation of the regular 5-simplex. There are unique 2 degrees

In geometry, a Lambert quadrilateral (also known as Ibn al-Haytham–Lambert quadrilateral), is a quadrilateral in which three of its angles are right angles

geometry, a polygon in the unitary plane, which has two complex dimensions. In computer graphics, a polygon whose boundary is not simple. In geometry

Centerpoint (alternatively spelled centrepoint) may refer to: Centerpoint (geometry), a generalization of the median to two or more dimensions CenterPoint Energy

McDuff was the first recipient of the award, for her work on symplectic geometry. A joint award was given for the first time in 2001, when Karen E. Smith

In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. Here, "vertex-transitive" means

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its

In geometry, a conchoid is a curve derived from a fixed point O, another curve, and a length d. It was invented by the ancient Greek mathematician Nicomedes

In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples

In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube. There are 5 degrees of rectifications

category of coherent sheaves is constructed using tools from complex geometry, a branch of mathematics that describes geometric shapes in algebraic terms

In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may

In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically

In algebraic geometry, a Fano variety, introduced by Gino Fano (Fano 1934, 1942), is an algebraic variety that generalizes certain aspects of complete

In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to

In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is

In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such that there is a dominant inseparable

Charlotte's Web, a children's novel by E. B. White (1952) Web (differential geometry), a type of set allowing an intrinsic Riemannian-geometry characterisation

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent

In geometry, a supporting line L of a curve C in the plane is a line that contains a point of C, but does not separate any two points of C. In other words

In mathematics, particularly in the subfield of real analytic geometry, a subanalytic set is a set of points (for example in Euclidean space) defined

In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube. There are four unique truncations

of contact between two algebraic or analytic varieties in algebraic geometry. A field with a valuation on it is called a valued field. One starts with

In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map, from a Riemann surface into

In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than

In geometry, a tetragonal trapezohedron, or deltohedron, is the second in an infinite series of trapezohedra, which are dual to the antiprisms. It has

In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety. The Mori program showed that 3-folds have minimal models. Matsuki,

than general ones, and Hensel's lemma applies to them. In algebraic geometry, a completion of a ring of functions R on a space X concentrates on a formal

In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines,

In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonal tiling on the

In geometry, a hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective

In geometry, a Bricard octahedron is a member of a family of flexible polyhedra constructed by Raoul Bricard in 1897. The overall shape of one of these

In geometry, a polyominoid (or minoid for short) is a set of equal squares in 3D space, joined edge to edge at 90- or 180-degree angles. The polyominoids

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex. There are four unique

In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri

In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete

integrability) the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) the explicit determination

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three

In geometry, a normal plane is any plane containing the normal vector of a surface at a particular point. The normal plane also refers to the plane that

In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section. Polar

In mathematics, specifically algebraic geometry, a period or algebraic period is a complex number that can be expressed as an integral of an algebraic

In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex. There are unique

In geometry, a normal plane is any plane containing the normal vector of a surface at a particular point. The normal plane also refers to the plane that

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a

self-closing, to the side away from the pasture (livestock field), by hinge geometry, a spring or weight.[citation needed] The gate may be made large enough

In geometry, a hyperpyramid is a generalisation of the normal pyramid to n dimensions. In the case of the pyramid one connects all vertices of the base

In the mathematical field of differential geometry, a geometric flow, also called a geometric evolution equation, is a type of partial differential equation

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the

In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex

In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created

In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex. The

picture from the wrong position gives a perceived distortion Perspective (geometry), a relation between geometric figures Vue d'optique or perspective view

In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex. There are 6 cantellation

In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional

In geometry, a d-dimensional simple polytope is a d-dimensional polytope each of whose vertices are adjacent to exactly d edges (also d facets). The vertex

circle must be replaced with the hyperbola for purposes of analytic geometry. A prominent instance is the depiction of spacetime as a pseudo-Euclidean

In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube. There are unique 6 degrees

In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor

other words by extending to algebraic curves generally with Cartesian geometry a basic concept from differential geometry, it represented a major advance

In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties

(Grades 7-8 or 8–9), one unit of Geometry or Investigating Geometry or Geometry A & B (Grades 8-9 or 9–10), one unit of Algebra II, fourth math unit range

In geometry, a negative pedal curve is a plane curve that can be constructed from another plane curve C and a fixed point P. For each point X ≠ P on the

or on the graph Convex conjugate, of a function Convexity (algebraic geometry), a restrictive technical condition for algebraic varieties originally introduced

In geometry, a bicone or dicone (from Latin: bi-, and Greek: di-, both meaning "two") is the three-dimensional surface of revolution of a rhombus around

City BDP Quadrangle, Toronto, Canada Complete quadrangle (projective geometry), a configuration with four points and six lines Love quadrangle, variant

In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational

In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a

In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane

In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers. Chow's

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter

In geometry, a rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope). It is one of 18 convex uniform polyhedral prisms

In differential geometry, a discipline within mathematics, a distribution on a manifold M {\displaystyle M} is an assignment x ↦ Δ x ⊆ T x M {\displaystyle

Look up generatrix in Wiktionary, the free dictionary. In geometry, a generatrix (/dʒɛnəˈreɪtrɪks/) or describent is a point, curve or surface that, when

In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube. There are 8 cantellations

In geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both

In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: D d = φ = 1 + 5 2 ≈ 1.618   034 {\displaystyle {D \over d}=\varphi

In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and centers of these

and outer distribution, in coding theory Distribution (differential geometry), a subset of the tangent bundle of a manifold Distributed parameter system

In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction

the basic unit of (volatile or non-volatile) computer memory Cell (geometry), a three-dimensional element, part of a higher-dimensional object Cell,

In mathematics, more precisely in differential geometry, a soldering (or sometimes solder form) of a fiber bundle to a smooth manifold is a manner of

In geometry, a truncated 120-cell is a uniform 4-polytope formed as the truncation of the regular 120-cell. There are three truncations, including a bitruncation

In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure

Three centroidal Voronoi tessellations of five points in a square In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation

In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex

In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular

In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube. There

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of

"Appendix A. Linear Algebra from a Geometric Point of View". Differential Geometry: A Geometric Introduction. Ithaca, NY: David W. Henderson. 2013. pp. 121–138

In computer graphics and computational geometry, a bounding volume (or bounding region) for a set of objects is a closed region that completely contains

Three centroidal Voronoi tessellations of five points in a square In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation

In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon

In geometry, a hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of

possible is described by Chazelle & Dobkin (1985). According to Euclidean geometry, a triangle can never be concave, but there exist concave polygons with

In (polyhedral) geometry, a flag is a sequence of faces of a polytope, each contained in the next, with exactly one face from each dimension. More formally

In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a

In four-dimensional geometry, a runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation)

In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection

In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique

In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective

In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell. E. L. Elte identified it in 1912 as a semiregular

In Euclidean geometry, a splitter is a line segment through one of the vertices of a triangle (that is, a cevian) that bisects the perimeter of the triangle

In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the

In four-dimensional geometry, a runcinated 24-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 24-cell

In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are

vertices. Thus, it is analogous to the definition of a convex set in geometry, a set that contains the line segment between every pair of its points.

structures is sometimes termed Möbius geometry, and is a type of Klein geometry. A conformal manifold is a Riemannian manifold (or pseudo-Riemannian manifold)

In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. Medians and angle bisectors

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings

In geometry, a surface S in 3-dimensional Euclidean space is ruled (also called a scroll) if through every point of S, there is a straight line that lies

In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed

In hyperbolic geometry, a horocycle (from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant

In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} that is invariant under

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal,

In algebraic geometry, a moduli scheme is a moduli space that exists in the category of schemes developed by French mathematician Alexander Grothendieck

In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving

or arcs in Wiktionary, the free dictionary. Arc may refer to: Arc (geometry), a segment of a differentiable curve Circular arc, a segment of a circle

In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all Intersection in exactly one point Intersection in two points

In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles

In four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell

In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube. Cantellated 6-demicube Cantellated

In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Every smooth scheme is regular, and every

In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also

In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such

In physics and geometry, a catenary (US: /ˈkætəˌnɛri/ KAT-ə-nerr-ee, UK: /kəˈtiːnəri/ kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable

In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique

In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")

In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic

free dictionary. Vertex, vertices or vertexes may refer to: Vertex (geometry), a point where two or more curves, lines, or edges meet Vertex (computer

In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis.

In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces. Some authors call a proper variety

In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form

In geometry, a hexagonal trapezohedron or deltohedron is the fourth in an infinite series of trapezohedra which are dual polyhedra to the antiprisms.

In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex.

In algebraic geometry, a Kummer quartic surface, first studied by Ernst Kummer (1864), is an irreducible nodal surface of degree 4 in P 3 {\displaystyle

In relativity and in pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length

In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral

In four-dimensional geometry, a cantellated tesseract is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular tesseract

In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex.

In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G

In algebraic geometry, a closed immersion of schemes is a morphism of schemes f : Z → X {\displaystyle f:Z\to X} that identifies Z as a closed subset

in optics The reach of information hiding, in computing Visibility (geometry), a geometric abstraction of real-life visibility Visible spectrum, the portion

In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell. There are two

comic book character who is the former mentor of the New Warriors Chord (geometry), a line segment joining two points on a curve Chord (graph theory), an edge

In geometry a conoid (from Greek κωνος  'cone' and -ειδης  'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1)

(exponentiation), the number b in an expression of the form bx Base (geometry), a side of a plane figure (for example a triangle) or face of a solid Base

that time he was interested in connections between combinatorics and geometry. A workshop on combinatorial geometry, held in Marseilles in April 2013

In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety

A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines

In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial

In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose generators are parallel

In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example

In eight-dimensional geometry, a pentellated 8-simplex is a convex uniform 8-polytope with 5th order truncations of the regular 8-simplex. There are two

abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of simple

In algebraic geometry, a Barth surface is one of the complex nodal surfaces in 3 dimensions with large numbers of double points found by Wolf Barth (1996)

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex

In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertices are concyclic is called a

In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics

rational function in geometry and complex analysis Möbius configuration, in geometry, a certain configuration in Euclidean space or projective space, consisting

X^{n}/{\mathfrak {S}}_{n}} , as in the beginning of this article. In algebraic geometry, a symmetric power is defined in a way similar to that in algebraic topology

In differential geometry, a Richmond surface is a minimal surface first described by Herbert William Richmond in 1904. It is a family of surfaces with

In conformal differential geometry, a conformal connection is a Cartan connection on an n-dimensional manifold M arising as a deformation of the Klein

In algebraic geometry, a birational invariant is a property that is preserved under birational equivalence. A birational invariant is a quantity or object

In seven-dimensional geometry, a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube

In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions

In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 nodes. The first examples were constructed by Eugenio G. Togliatti (1940)

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube. There

In algebraic geometry a normal crossing singularity is a singularity similar to a union of coordinate hyperplanes. The term can be confusing because normal

In algebraic geometry, a Deligne–Mumford stack is a stack F such that the diagonal morphism F → F × F {\displaystyle F\to F\times F} is representable

In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings

In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation r = a sin ⁡ θ θ , {\displaystyle

troops against the Avars Lune (geometry), a 2-dimensional arc-defined convex-concave area Lune of Hippocrates, in geometry, a plane region bounded by arcs

In five-dimensional geometry, a cantellated 5-simplex is a convex uniform 5-polytope, being a cantellation of the regular 5-simplex. There are unique

In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope. Truncated 6-demicube Truncaced demihexeract Truncated

the crystal lattice glide along each other, changing the material's geometry. A critical resolved shear stress is required to initiate a slip. Slip in

In geometry, a quadratrix (from Latin quadrator 'squarer') is a curve having ordinates which are a measure of the area (or quadrature) of another curve

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called

In geometry, a group of isometries of hyperbolic space is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold

In geometry, a zonogon is a centrally-symmetric, convex polygon. Equivalently, it is a convex polygon whose sides can be grouped into parallel pairs with

In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points

In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted)

In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six

In projective geometry, a special conformal transformation is a linear fractional transformation that is not an affine transformation. Thus the generation

the band And One Flop (album), by Maurizio Pisciottu Flop (algebraic geometry), a birational transformation Flop-transition, in the string theory of physics

In algebraic geometry a generalized Jacobian is a commutative algebraic group associated to a curve with a divisor, generalizing the Jacobian variety of

In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell. There are two

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from

In algebraic geometry, a morphism f : X → S {\displaystyle f:X\to S} between schemes is said to be smooth if (i) it is locally of finite presentation

In algebraic geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn]

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from

In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism

Asher Perles (Hebrew: מיכה פרלס) is an Israeli mathematician working in geometry, a professor emeritus at the Hebrew University. He earned his Ph.D. in 1964

In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex. There are 8 cantellation

In seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube. There are 10 degrees of

In mathematics, in particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties

In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms

In algebraic geometry, a tetrahedroid (or tétraédroïde) is a special kind of Kummer surface studied by Cayley (1846), with the property that the intersections

In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments

sophist Protagoras, with whom he claims to have studied before turning to geometry. A dubious tradition repeated among ancient biographers like Diogenes Laërtius

In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary

In seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 2 unique forms. A runcic 7-cube

In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are

In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking

In five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex

(named after Jakob Steiner) may refer to: Steiner point (computational geometry), a point added in solving a geometric optimization problem to make its solution

containing all of these objects. Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several

In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also

In algebraic geometry, a Weddle surface, introduced by Thomas Weddle (1850, footnote on page 69), is a quartic surface in 3-dimensional projective space

In geometry, a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane

In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These

In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named

In algebraic geometry, a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity

operator algebra in local quantum field theory ε-net (computational geometry), a concept approximating a general sets with a collection of simpler subsets

In projective geometry, a plane at infinity is the hyperplane at infinity of a three dimensional projective space or to any plane contained in the hyperplane

In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as

In geometry, a space-filling polyhedron is a polyhedron that can be used to fill all of three-dimensional space via translations, rotations and/or reflections

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature

In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation

In eight-dimensional geometry, a rectified 8-orthoplex is a convex uniform 8-polytope, being a rectification of the regular 8-orthoplex. There are unique

In geometry, a snub polyhedron is a polyhedron obtained by performing a snub operation: alternating a corresponding omnitruncated or truncated polyhedron

In four-dimensional geometry, a cantellated 120-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 120-cell

In six-dimensional geometry, a runcic 5-cube or (runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope. There are 2 runcic forms for the

In Riemannian geometry, a Jacobi field is a vector field along a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference

In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i

In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which

In seven-dimensional geometry, a rectified 7-orthoplex is a convex uniform 7-polytope, being a rectification of the regular 7-orthoplex. There are unique

In algebraic geometry, a Coble surface was defined by Dolgachev & Zhang (2001) to be a smooth rational projective surface with empty anti-canonical linear

In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology. In set theory

In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles

In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly

In seven-dimensional geometry, a cantic 7-cube or truncated 7-demicube as a uniform 7-polytope, being a truncation of the 7-demicube. A uniform 7-polytope

In geometry, a glissette is a curve determined by either the locus of any point, or the envelope of any line or curve, that is attached to a curve that

q(v) = 0; such a v is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an

In seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex. There are unique

In algebraic geometry, a chordal variety of a variety is the union of all the chords (lines meeting 2 points), including the limiting cases of tangent