A shape or figure 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 type. A plane shape, two-dimensional shape, or 2D shape ( plane figure, two-dimensional figure, or 2D figure) is constrained to lie on a plane, in contrast to solid figures.
Other common shapes are points, lines, planes, and conic sections such as , , and .
Among the most common 3-dimensional shapes are polyhedra, which are shapes with flat faces; , which are egg-shaped or sphere-shaped objects; cylinders; and .
If an object falls into one of these categories exactly or even approximately, we can use it to describe the shape of the object. Thus, we say that the shape of a manhole cover is a disk, because it is approximately the same geometric object as an actual geometric disk.
Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called and include , , and . Other shapes may be bounded by 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 faces enclosed by those lines, as well as the resulting interior points. Such shapes are called and include as well as pyramids such as . 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 if all of the points on a line segment between any two of its points are also part of the shape.
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 objects such as a point, a line, a curve, a plane, a plane figure (e.g. 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 – in which case they may be analyzed by differential geometry, or as .
In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. ... We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scaleHere, scale means only uniform scaling, as non-uniform scaling would change the shape of the object (e.g., it would turn a square into a rectangle). and rotational effects are filtered out from an object.’
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 and placement in space of the object. For instance, a " d" and a " p" have the same shape, as they can be perfectly superimposed if the " d" is translated to the right by a given distance, rotated upside down and magnified by a given factor (see Procrustes superimposition for details). However, a mirror image could be called a different shape. For instance, a " b" and a " p" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written. Even though they have the same size, there's no way to perfectly superimpose them by translating and rotating them along the page. Similarly, within a three-dimensional space, a right hand and a left hand have a different shape, even if they are the mirror images of each other. Shapes may change if the object is scaled non-uniformly. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal directions. In other words, preserving axes of symmetry (if they exist) is important for preserving shapes. Also, shape is determined by only the outer boundary of an object.
Objects that have the same shape or mirror image shapes are called geometrically similar, whether or not they have the same size. Thus, objects that can be transformed into each other by rigid transformations, mirroring, and uniform scaling are similar. Similarity is preserved when one of the objects is uniformly scaled, while congruence is not. Thus, congruent objects are always geometrically similar, but similar objects may not be congruent, as they may have different size.
One way of modeling non-rigid movements is by . Roughly speaking, a homeomorphism is a continuous stretching and bending of an object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not. An often-repeated mathematical joke is that topologists cannot tell their coffee cup from their donut,
A described shape has external lines that you can see and make up the shape. If you were putting you coordinates on and coordinate graph you could draw lines to show where you can see a shape, however not every time you put coordinates in a graph as such you can make a shape. This shape has a outline and boundary so you can see it and is not just regular dots on a regular paper.
the shape of triangle ( u, v, w). Then the shape of the equilateral triangle is