152 relations: Absolute value, Abstract polytope, Angle, Angle trisection, Antiparallelogram, Apeirogon, Apothem, Area, Basalt, Bee, Biology, Boolean operations on polygons, Caere, California, Capitoline Museums, Cartesian coordinate system, Cartography, Centroid, Charles Sanders Peirce, Chiliagon, Circle, Circumscribed circle, Compass-and-straightedge construction, Complete graph, Complex number, Complex plane, Complex polygon, Complex polytope, Computational geometry, Computer graphics, Concave polygon, Configuration (polytope), Constructible polygon, Convex polygon, Crystal, David Hume, Decagon, Degree (angle), Devils Postpile National Monument, Digon, Dodecagon, Edge (geometry), Enneacontagon, Enneadecagon, Equiangular polygon, Equilateral polygon, Euclidean geometry, Geoffrey Colin Shephard, Geometric primitive, Geometric shape, ..., Geometry, Giant's Causeway, Golygon, Greek language, Group action, Harold Scott MacDonald Coxeter, Hectogon, Hendecagon, Heptacontagon, Heptadecagon, Heptagon, Hexacontagon, Hexadecagon, Hexagon, Hexagonal tiling, Hilbert space, Honeycomb, Icosagon, Icositetragon, Imaginary number, Immanuel Kant, Incircle and excircles of a triangle, Internal and external angles, Isogonal figure, Isoperimetric inequality, Isotoxal figure, Johannes Kepler, John Horton Conway, Kepler–Poinsot polyhedron, Krater, Late Latin, Lava, Line segment, List of self-intersecting polygons, Materials system, Meditations on First Philosophy, Megagon, Monogon, Monotone polygon, Myriagon, Neusis construction, Nonagon, Northern Ireland, Numeral prefix, Octacontagon, Octadecagon, Octagon, Orbit (dynamics), Orthogonality, Partially ordered set, Pentacontagon, Pentadecagon, Pentagon, Pentagram, Petrie polygon, Pi, Pick's theorem, Plane (geometry), Point in polygon, Polyform, Polygon mesh, Polygon soup, Polygon triangulation, Polygonal chain, Polyhedron, Polytope, Quadrilateral, Quasiregular polyhedron, Radian, Real number, Rectilinear polygon, Regular polygon, Regular Polytopes (book), René Descartes, Shape, Shoelace formula, Simple polygon, Skew apeirogon, Skew polygon, Spherical trigonometry, Square tiling, Star polygon, Star-shaped polygon, Synthetic geometry, Tangential polygon, Tessellation, Tetracontagon, Tetradecagon, Thomas Bradwardine, Tiling puzzle, Triacontagon, Triangle, Triangular tiling, Tridecagon, Turn (geometry), Uniform polyhedron, Vertex (computer graphics), Vertex (geometry), Wallace–Bolyai–Gerwien theorem, Wythoff construction, 257-gon, 65537-gon. Expand index (102 more) » « Shrink index
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
In geometry, an antiparallelogram is a quadrilateral having, like a parallelogram, two opposite pairs of equal-length sides, but in which the sides of one pair cross each other.
In geometry, an apeirogon (from the Greek word ἄπειρος apeiros, "infinite, boundless" and γωνία gonia, "angle") is a generalized polygon with a countably infinite number of sides.
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides.
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
Basalt is a common extrusive igneous (volcanic) rock formed from the rapid cooling of basaltic lava exposed at or very near the surface of a planet or moon.
Bees are flying insects closely related to wasps and ants, known for their role in pollination and, in the case of the best-known bee species, the European honey bee, for producing honey and beeswax.
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR,...) operating on one or more sets of polygons in computer graphics.
: Caere (also Caisra and Cisra) is the Latin name given by the Romans to one of the larger cities of Southern Etruria, the modern Cerveteri, approximately 50-60 kilometres north-northwest of Rome.
California is a state in the Pacific Region of the United States.
The Capitoline Museums (Italian: Musei Capitolini) are a single museum containing a group of art and archaeological museums in Piazza del Campidoglio, on top of the Capitoline Hill in Rome, Italy.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartography (from Greek χάρτης chartēs, "papyrus, sheet of paper, map"; and γράφειν graphein, "write") is the study and practice of making maps.
In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.
Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".
In geometry, a chiliagon or 1000-gon is a polygon with 1000 sides.
A circle is a simple closed shape.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
The term complex polygon can mean two different things.
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
Computer graphics are pictures and films created using computers.
A simple polygon that is not convex is called concave, non-convex or reentrant.
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.
David Hume (born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist, who is best known today for his highly influential system of philosophical empiricism, skepticism, and naturalism.
In geometry, a decagon is a ten-sided polygon or 10-gon.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
Devils Postpile National Monument is a National Monument located near Mammoth Mountain in eastern California.
In geometry, a digon is a polygon with two sides (edges) and two vertices.
In geometry, a dodecagon or 12-gon is any twelve-sided polygon.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
In geometry, an enneacontagon or enenecontagon or 90-gon (from Ancient Greek ἑννενήκοντα, ninety) is a ninety-sided polygon.
In geometry an enneadecagon or 19-gon is a nineteen-sided polygon.
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal.
In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups.
The term geometric primitive, or prim, in computer graphics and CAD systems is used in various senses, with the common meaning of the simplest (i.e. 'atomic' or irreducible) geometric objects that the system can handle (draw, store).
A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object.
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
The Giant's Causeway is an area of about 40,000 interlocking basalt columns, the result of an ancient volcanic fissure eruption.
A golygon is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths.
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon.
In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon.
In geometry, a heptacontagon (or hebdomecontagon from Ancient Greek ἑβδομήκοντα, seventy) or 70-gon is a seventy-sided polygon.
In geometry, a heptadecagon or 17-gon is a seventeen-sided polygon.
In geometry, a heptagon is a seven-sided polygon or 7-gon.
In geometry, a hexacontagon or hexecontagon or 60-gon is a sixty-sided polygon.
In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen.
In geometry, an icosagon or 20-gon is a twenty-sided polygon.
In geometry, an icositetragon (or icosikaitetragon or tetracosagon) or 24-gon is a twenty-four-sided polygon.
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.
Immanuel Kant (22 April 1724 – 12 February 1804) was a German philosopher who is a central figure in modern philosophy.
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.
In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
A krater or crater (κρατήρ, kratēr,."mixing vessel") was a large vase in Ancient Greece, particularly used for watering down wine.
Late Latin is the scholarly name for the written Latin of Late Antiquity.
Lava is molten rock generated by geothermal energy and expelled through fractures in planetary crust or in an eruption, usually at temperatures from.
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.
In Computer graphics, Materials are an enhancement of texture mapping (and a pre-requisite for advanced shading effects) that allows for objects in 3D modelling packages and video games to simulate different types of materials in real life.
Meditations on First Philosophy —The original Meditations, translated, in its entirety.
A megagon or 1 000 000-gon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great").
In geometry a monogon is a polygon with one edge and one vertex.
In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects P at most twice.
In geometry, a myriagon or 10000-gon is a polygon with 10000 sides.
The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.
In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.
Northern Ireland (Tuaisceart Éireann; Ulster-Scots: Norlin Airlann) is a part of the United Kingdom in the north-east of the island of Ireland, variously described as a country, province or region.
Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.
In geometry, an octacontagon (or ogdoëcontagon or 80-gon from Ancient Greek ὁγδοήκοντα, eighty) is an eighty-sided polygon.
An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system.
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
In geometry, a pentacontagon or pentecontagon or 50-gon is a fifty-sided polygon.
In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.
In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.
A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.
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 of the facets.
The number is a mathematical constant.
Given a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points, Pick's theorem provides a simple formula for calculating the area of this polygon in terms of the number of lattice points in the interior located in the polygon and the number of lattice points on the boundary placed on the polygon's perimeter: In the example shown, we have interior points and boundary points, so the area is.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon.
In recreational mathematics, a polyform is a plane figure constructed by joining together identical basic polygons.
A polygon mesh is a collection of, s and s that defines the shape of a polyhedral object in 3D computer graphics and solid modeling.
A polygon soup is a group of unorganized triangles, with generally no relationship whatsoever.
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, Chapter 3: Polygon Triangulation: pp.45–61.
In geometry, a polygonal chain is a connected series of line segments.
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
In elementary geometry, a polytope is a geometric object with "flat" sides.
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.
In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
A rectilinear polygon is a polygon all of whose edge intersections are at right angles.
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material composition.
The shoelace formula or shoelace algorithm (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.
In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.
In geometry, an infinite skew polygon (or skew apeirogon) has vertices that are not all colinear.
In geometry, a skew polygon is a polygon whose vertices are not all coplanar.
Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.
In geometry, a star polygon is a type of non-convex polygon.
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 polygon boundary is visible.
Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.
In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
In geometry, a tetracontagon or tessaracontagon is a forty-sided polygon or 40-gon.
In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.
Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury.
Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps).
In geometry, a triacontagon or 30-gon is a thirty-sided polygon.
A triangle is a polygon with three edges and three vertices.
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.
In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.
A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
A vertex (plural vertices) in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space, at multiple points on a surface.
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and Paul Gerwien, is a theorem related to dissections of polygons.
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 257-gon (diacosipentacontaheptagon, diacosipentecontaheptagon) is a polygon with 257 sides.
In geometry, a 65537-gon is a polygon with 65537 sides.
2-dimensional polytope, 2-polytope, Adjacent side (polygon), All the 2d shapes, Area of a polygon, Convex & concave polygons, Convex and concave polygons, Coptic polygon, Diacosigon, Dihectagon, Dihectapentacontakaiheptagon, Dischiliagon, Enacosigon, Enakischiliagon, Enneahectagon, Hecatogon, Heptacosigon, Heptahectagon, Heptakischiliagon, Hexacosigon, Hexahectagon, Hexakischiliagon, Icosimonogon, Irregular polygon, Irregular polygons, N-gon, N-gons, Names of Polygons, Ngon, Nonacoptic polygon, Octacosigon, Octahectagon, Octakischiliagon, Pentacosigon, Pentahectagon, Pentakischiliagon, Polygon Diagonal, Polygon Diameter, Polygon Edge, Polygon Vertex, Polygon area, Polygon diagonal, Polygon diameter, Polygon edge, Polygon vertex, Polygonal, Polygonal area, Polygonal region, Polygons, Regular Nonagon, Tetracosigon, Tetrahectagon, Tetrakischiliagon, Tricosagon, Trihectagon, Trischiliagon.