  Communication
Free Faster access than browser!

Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit. 

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, ... Expand index (102 more) »

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

Abstract polytope

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.

Angle

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.

New!!: Polygon and Angle · See more »

Angle trisection

Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.

Antiparallelogram

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.

Apeirogon

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.

Apothem

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

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

New!!: Polygon and Area · See more »

Basalt

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.

New!!: Polygon and Basalt · See more »

Bee

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.

New!!: Polygon and Bee · See more »

Biology

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

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

: 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.

New!!: Polygon and Caere · See more »

California

California is a state in the Pacific Region of the United States.

Capitoline Museums

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.

Cartesian coordinate system

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

Cartography (from Greek χάρτης chartēs, "papyrus, sheet of paper, map"; and γράφειν graphein, "write") is the study and practice of making maps.

Centroid

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

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".

Chiliagon

In geometry, a chiliagon or 1000-gon is a polygon with 1000 sides.

Circle

A circle is a simple closed shape.

New!!: Polygon and Circle · See more »

Circumscribed circle

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

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.

No description.

Complex number

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.

Complex plane

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.

Complex polygon

The term complex polygon can mean two different things.

Complex polytope

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

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

Computer graphics

Computer graphics are pictures and films created using computers.

Concave polygon

A simple polygon that is not convex is called concave, non-convex or reentrant.

Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.

Convex polygon

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.

Crystal

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

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.

Decagon

In geometry, a decagon is a ten-sided polygon or 10-gon.

Degree (angle)

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

Devils Postpile National Monument is a National Monument located near Mammoth Mountain in eastern California.

Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

New!!: Polygon and Digon · See more »

Dodecagon

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

Enneacontagon

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.

Equiangular polygon

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal.

Equilateral polygon

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

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

Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups.

Geometric primitive

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).

Geometric shape

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

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.

Giant's Causeway

The Giant's Causeway is an area of about 40,000 interlocking basalt columns, the result of an ancient volcanic fissure eruption.

Golygon

A golygon is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths.

Greek language

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.

Group action

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 Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

Hectogon

In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon.

Hendecagon

In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon.

Heptacontagon

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.

Heptagon

In geometry, a heptagon is a seven-sided polygon or 7-gon.

Hexacontagon

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.

Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

Honeycomb

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.

Icosagon

In geometry, an icosagon or 20-gon is a twenty-sided polygon.

Icositetragon

In geometry, an icositetragon (or icosikaitetragon or tetracosagon) or 24-gon is a twenty-four-sided polygon.

Imaginary number

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

Immanuel Kant (22 April 1724 – 12 February 1804) was a German philosopher who is a central figure in modern philosophy.

Incircle and excircles of a triangle

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.

Internal and external angles

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

Isogonal figure

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.

Isoperimetric inequality

In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.

Isotoxal figure

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

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

John Horton Conway

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.

Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

Krater

A krater or crater (κρατήρ, kratēr,."mixing vessel") was a large vase in Ancient Greece, particularly used for watering down wine.

New!!: Polygon and Krater · See more »

Late Latin

Late Latin is the scholarly name for the written Latin of Late Antiquity.

Lava

Lava is molten rock generated by geothermal energy and expelled through fractures in planetary crust or in an eruption, usually at temperatures from.

New!!: Polygon and Lava · See more »

Line segment

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.

List of self-intersecting polygons

Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.

Materials system

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

Meditations on First Philosophy —The original Meditations, translated, in its entirety.

Megagon

A megagon or 1 000 000-gon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great").

Monogon

In geometry a monogon is a polygon with one edge and one vertex.

Monotone polygon

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.

Myriagon

In geometry, a myriagon or 10000-gon is a polygon with 10000 sides.

Neusis construction

The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.

Nonagon

In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.

Northern Ireland

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 prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.

Octacontagon

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.

Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

Orbit (dynamics)

In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system.

Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

Partially ordered set

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.

Pentacontagon

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.

Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

Pentagram

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.

Petrie polygon

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.

Pi

The number is a mathematical constant.

New!!: Polygon and Pi · See more »

Pick's theorem

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.

Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

Point in polygon

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.

Polyform

In recreational mathematics, a polyform is a plane figure constructed by joining together identical basic polygons.

Polygon mesh

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.

Polygon soup

A polygon soup is a group of unorganized triangles, with generally no relationship whatsoever.

Polygon triangulation

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.

Polygonal chain

In geometry, a polygonal chain is a connected series of line segments.

Polyhedron

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.

Polytope

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.

Quasiregular polyhedron

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.

New!!: Polygon and Radian · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

Rectilinear polygon

A rectilinear polygon is a polygon all of whose edge intersections are at right angles.

Regular polygon

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 (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

Shape

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.

New!!: Polygon and Shape · See more »

Shoelace formula

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.

Simple polygon

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.

Skew apeirogon

In geometry, an infinite skew polygon (or skew apeirogon) has vertices that are not all colinear.

Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

Spherical trigonometry

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.

Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

Star polygon

In geometry, a star polygon is a type of non-convex polygon.

Star-shaped 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

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

Tangential polygon

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).

Tessellation

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.

Tetracontagon

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 puzzle

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).

Triacontagon

In geometry, a triacontagon or 30-gon is a thirty-sided polygon.

Triangle

A triangle is a polygon with three edges and three vertices.

Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

Tridecagon

In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.

Turn (geometry)

A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.

Uniform polyhedron

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).

Vertex (computer graphics)

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.

Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

Wallace–Bolyai–Gerwien theorem

In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and Paul Gerwien, is a theorem related to dissections of polygons.

Wythoff construction

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

257-gon

In geometry, a 257-gon (diacosipentacontaheptagon, diacosipentecontaheptagon) is a polygon with 257 sides.

65537-gon

In geometry, a 65537-gon is a polygon with 65537 sides.

References

Hey! We are on Facebook now! »