Pyramids are a type of polyhedron that has a polygonal base with triangles extending from it to form an apex. The pyramids of Egypt would be examples of square pyramids because the bottom of them are squares. Likewise, you could have a pentagonal pyramid, hexagonal pyramid, pentagrammic pyramid etc.
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In ancient egypt, pharoes were placed in great pyramids, which served as a tumb. these pyramids were magnifacent, and there were no mistakes made on them. the archatects eventually learned geometry to have the right proportions for the pyramids, and other mathimatical needs
Pyramids and cubes are examples of prisms. You can see more examples and pictures at http://www.mathsisfun.com/geometry/prisms.html
pyramids are triangular because of some religious reasons which include stairway to heaven,protection of spirits and all... .According to geometry triangular shapes are more durable and can stand longer,more easy to build...
Plane Geometry (is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper) Solid Geometry (is about three dimensional objects like cubes and pyramids).
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few