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This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
The second series, which is again aimed at four- to five-year-olds, comprised five episodes, focusing on the four basic two-dimensional shapes; each episode would open with Lolita standing by a mobile with the four basic shapes hanging from it and singing the series' main theme, Squares and Triangles, Circles and Rectangles as the mobile began ...
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 points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points.
Two-dimensional spaces can also be curved, for example the sphere and hyperbolic plane, sufficiently small portions of which appear like the flat plane, but on which straight lines which are locally parallel do not stay equidistant from each-other but eventually converge or diverge, respectively.
Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis ...
In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical.
The four quadrants of a Cartesian coordinate system. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
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