Editing Shape (section)

==In geometry==
[[File:Area.svg|thumb|250px|A set of geometric shapes in 2 dimensions: [[parallelogram]], [[triangle]] & [[circle]]]]
[[File:Basic shapes.svg|thumb|250px|A set of geometric shapes in 3 dimensions: [[Pyramid (geometry)|pyramid]], [[sphere]] & [[cube]]]]

A '''geometric shape''' consists of the [[Geometry|geometric]] information which remains when [[Translation (geometry)|location]], [[Scaling (geometry)|scale]], [[Orientation (geometry)|orientation]] and [[reflection (geometry)|reflection]] are removed from the description of a [[geometric object]].<ref name=Kendall>{{cite journal|
doi = 10.1112/blms/16.2.81|
author = Kendall, D.G.|
title = Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces|
journal = Bulletin of the London Mathematical Society|
year = 1984|
volume = 16|
issue = 2|
pages = 81–121}}</ref> That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape.

Many two-dimensional geometric shapes can be defined by a set of [[Point (geometry)|points]] or [[Vertex (geometry)|vertices]] and [[line (geometry)|lines]] connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called [[polygon]]s and include [[triangle]]s, [[square]]s, and [[pentagon]]s. Other shapes may be bounded by [[curve]]s such as the [[circle]] or the [[ellipse]]. 

Many three-dimensional geometric shapes can be defined by a set of vertices, lines connecting the vertices, and two-dimensional [[Face (geometry)|faces]] enclosed by those lines, as well as the resulting interior points. Such shapes are called [[polyhedron]]s 
and include [[cube]]s as well as [[Pyramid (geometry)|pyramids]] such as [[tetrahedron]]s. Other three-dimensional shapes may be bounded by curved surfaces, such as the [[ellipsoid]] and the [[sphere]].

A shape is said to be [[Convex polytope|convex]] if all of the points on a line segment between any two of its points are also part of the shape.

===Properties===
There are multiple ways to compare the shapes of two objects:
* [[Congruence (geometry)|Congruence]]: Two objects are ''congruent'' if one can be transformed into the other by a sequence of rotations, translations, and/or reflections.
* [[Similarity (geometry)|Similarity]]: Two objects are ''similar'' if one can be transformed into the other by a uniform scaling, together with a sequence of rotations, translations, and/or reflections.
* [[Homotopy#Isotopy|Isotopy]]: Two objects are ''isotopic'' if one can be transformed into the other by a sequence of [[Deformation (mechanics)|deformations]] that do not tear the object or put holes in it.
[[Image:Similar-geometric-shapes.svg|thumb|300px|left|Figures shown in the same color have the same shape as each other and are said to be similar.]]
Sometimes, two similar or congruent objects may be regarded as having a different shape if a reflection is required to transform one into the other. For instance, the letters "'''b'''" and "'''d'''" are a reflection of each other, and hence they are congruent and similar, but in some contexts they are not regarded as having the same shape. Sometimes, only the outline or external boundary of the object is considered to determine its shape. For instance, a hollow sphere may be considered to have the same shape as a solid sphere. [[Procrustes analysis]] is used in many sciences to determine whether or not two objects have the same shape, or to measure the difference between two shapes. In advanced mathematics, [[quasi-isometry]] can be used as a criterion to state that two shapes are approximately the same.

Simple shapes can often be classified into basic [[geometry|geometric]] objects such as a [[line (geometry)|line]], a [[curve]], a [[plane (geometry)|plane]], a [[plane figure]] (e.g. [[square (geometry)|square]] or [[circle]]), or a solid figure (e.g. [[cube]] or [[sphere]]). However, most shapes occurring in the physical world are complex. Some, such as plant structures and coastlines, may be so complicated as to defy traditional mathematical description&nbsp;– in which case they may be analyzed by [[differential geometry]], or as [[fractal]]s.

Some common shapes include: [[Circle]], [[Square]], [[Triangle]], [[Rectangle]], [[Oval]], [[Star (polygon)]], [[Rhombus]], [[Semicircle]].
Regular polygons starting at pentagon follow the naming convention of the Greek derived prefix with '-gon' suffix: Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon... See [[polygon]]