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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 most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
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.
Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
In Figure 2, for instance, the pieces are polyominoes of consecutive sizes from 1 up to 9 units. The target is a 4 × 4 square with an inner square hole. Surprisingly, computer investigations show that Figure 2 is just one among 4,370 distinct 3 × 3 geomagic squares using pieces with these same sizes and same target.
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