- Shape
The

**shape**(OE. "sceap" Eng. "created thing") of an object located in some space refers to the part of space occupied by the object as determined by its external boundary — abstracting from other aspects the object may have such as its colour, content, or the substance of which it is composed, as well as from the object's position and orientation in space, and its size.Simple two-dimensional shapes can be described by basic

geometry such as points, line,curve s, plane, and so on. Shapes that occur in the physical world are often quite complex; they may be arbitrarily curved as studied bydifferential geometry , orfractal , as for plants or coastlines).**Rigid shape definition**In

geometry , two subsets of aEuclidean 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 scalings. 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 anequivalence class of subsets of a Euclidean space having the same shape.Shapes of physical objects are equal if the subsets of space these objects occupy satisfy the definition above. In particular, the shape does not depend on the size of the object nor on changes in orientation/direction. However, a

mirror image could be called a different shape. Shape may change if the object is scaled non uniformly. For example, asphere becomes anellipsoid when scaled differently in the vertical and horizontal direction. In other words, preserving axes ofsymmetry (if they exist) is important for preserving shapes. Also, shape is not necessary determined by only the outer boundary of an object. For example, a solid ice cube and a second ice cube containing an inner cavity (air bubble) do not necessarily have the same shape, even though the outer boundary is identical.Objects that can be transformed into each other only by rigid transformations and mirroring are congruent. An object is therefore congruent to its

mirror image (even if it is not symmetric), but not to a scaled version.Objects that have the same shape or one has the same shape as the other's mirror image (or both if they are themselves symmetric) are called geometrically similar. Thus congruent objects are always geometrically similar, but geometrical similarity additionally allows uniform scaling.**Non-rigid shape definition**A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality (e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions). By allowing also isometric (or near-isometric) deformations like bending, the intrinsic geometry of the object will stay the same, while subparts might be located at very different positions in space. This definition uses the fact, that

geodesic s (curves measured along the surface of the object) stay the same, independent of the isometricembedding . This means that the distance from a finger to a toe of a person measured along the body is always the same, no matter how the body is posed. An ant climbing a bendable plant will not notice how the wind moves it around, as only bending and no stretching is involved. It is true that when a body is bent, the wind moves around it, not through it.**Colloquial shape definition**Shape can also be more loosely defined as "the appearance of something, especially its outline". This definition is consistent with the above, in that the shape of a set does not depend on its position, size or orientation. However, it does not always imply an exact mathematical transformation. For example it is common to talk of "star-shaped" objects even though the number of points of the star is not defined.

**hape analysis**The modern definition of shape has arisen in the field of

statistical shape analysis . In particularProcrustes analysis , which is a technique for analysing the statistical distributions of shapes. These techniques have been used to examine thealignments of random points .**ee also***

List of geometric shapes

*Glossary of shapes with metaphorical names

*Form

*Morphology

*Equidimensional **External links*** [

*http://www.scribd.com/doc/1113/Thinking-about-sizes-and-shapes/ Answers for many questions related to shapes and sizes of common objects*]

* [*http://home.att.net/~amcnet2/album/shapes/intro.html American artist Allan McCollum's project to create a unique "shape" for every individual on the planet*]

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