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Shape

The ** shape ** (from [Old English] * ȝesceap * , * shap * , etc., originally meaning * created thing * ) of an object located in some space is the part of that space occupied by the object, as determined by its external boundary – abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties (position and orientation in space; size).

Mathematician and statistician [David George Kendall] defined shape this way:

Shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object.

Simple two-dimensional shapes can be described by basic [geometry] such as [point] s, [line] , [curve] s, [plane] , and so on. (A shape whose points belong all the same plane is called a * plane figure * .) Most shapes occurring in the physical world are complex. Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analysed by [differential geometry] , or as [fractals] .

** Rigid shape definition **

In [geometry] , two subsets of a [Euclidean space] have the same shape if one can be transformed to the other by a combination of [translations] , [rotation] s (together also called rigid transformations), and [uniform scaling] s. In other words, the * shape * of a set is all the geometrical information that is invariant to position (including rotation) and scale.

Having the same shape is an [equivalence relation] , and accordingly a precise mathematical definition of the notion of shape can be given as being an [equivalence class] of subsets of a Euclidean space having the same shape.

A polygon is a shape that is made of line segments that close at their endpoints, and sometimes harder.

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