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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.
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
Download as PDF; Printable version; In other projects Wikimedia Commons; Wiktionary; ... This includes all shapes that can also be found in the subcategories.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. [ 1 ] More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry , i.e., a combination of rigid motions , namely a ...
Other symmetry constructions of the rhombic dodecahedron are also space-filling, and as parallelotopes they are similar to variations of space-filling truncated octahedra. [12] For example, with 4 square faces, and 60-degree rhombic faces, and D 4h dihedral symmetry, order 16. It can be seen as a cuboctahedron with square pyramids attached on ...
A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral , the ...
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines , are statistically self-similar: parts of them show the same statistical properties at many scales. [ 2 ]
A spiral similarity taking triangle ABC to triangle A'B'C'. Spiral similarity is a plane transformation in mathematics composed of a rotation and a dilation. [1] It is used widely in Euclidean geometry to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and olympiads.
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