Pyramid

This article is about the polyhedron. For specific massive constructions in the shape of that polyhedron, see: Egyptian pyramids, Mesoamerican pyramids, Nubian pyramids.

A pyramid is a geometric shape formed by connecting a polygonal base and a point, called the apex, by triangular faces. When unspecified the base is usually assumed to be square. One of the Platonic solids, the tetrahedron, is a triangular pyramid. The square and pentagonal pyramids can also be constructed with all faces regular, and so count among the Johnson solids. All pyramids are self-dual. The volume of a pyramid is <math>V = \frac{1}{3} Ah<math> where A is the area of the base and h the height from the base to the apex. The geometric centre of a square-sided regular pyramid is located on the symmetry axis, one quarter of the way from the base to the apex.

Structures

The pyramids of Giza. The largest pyramids, from left to right, are Menkaure's pyramid, Khafre's pyramid, and the Great Pyramid.

Pyramid-shaped structures were built by many ancient peoples. The most famous are the Egyptian pyramids — huge pyramids built of brick or stone, used as tombs for pharaohs. The Great Pyramid of Giza is one of the Seven Wonders of the World, and the only one of the seven to survive into modern times. The ancient Egyptians smoothed the faces of their pyramids with gold and polished white limestone, though many of the stones used for the purpose have fallen out over the centuries.

To the south of Egypt the Nubians also built pyramids. They built far more than the Egyptians, but they are much smaller. The Nubian pyramids were constructed at a much steeper angle than Egyptian ones and were not tombs, but monuments to dead kings. Pyramids were built in Nubia up until the AD 300s.

The Mesopotamians also built pyramids called ziggurats, with a distinct series of layers. In ancient times these were brightly painted. Since they were constructed of mud-brick, little remains of them. The biblical Tower of Babel is believed to be a Babylonian ziggurat.

A number of Mesoamerican cultures also built pyramid-shaped structures. Mesoamerican pyramids were also usually stepped, with temples on top, more similar to the Mesopotamian ziggurat than the Egyptian pyramid. The largest pyramid by volume is the Great Pyramid of Cholula, in the Mexican state of Puebla.

There are other pyramid-shaped ancient monuments found in parts of Asia.

Pyramids were also found in Greece. One of these pyramids in Greece is older than the pyramid of Cheops, as it was dated to 2720 BC.

There is a pyramid in ancient Rome. The 27-meter-high pyramid of Gaius Cestius was built by the end of the first century BC and still exists today, close to the Porta San Paolo.

Modern pyramids

A modern pyramid, built as a feature and as an entrance to the Louvre Art Gallery

Missing image Csulb_pyramid.jpg The CSU Long Beach Pyramid.

An example of a modern pyramid can be found in Paris, France, in front of the Louvre Museum.

The gymnasium for the basketball and volleyball teams on the California State University, Long Beach, campus in California, United States, is an 18-story-tall blue pyramid.

The Luxor Hotel in Las Vegas, United States, is a 30-story pyramid.

Esoterism

Esoterists have attributed remarkable properties ("pyramid power") to the pyramid shape and remarkable histories to historical pyramids; even paper pyramids are reputedly able to keep blades sharp and to prevent meat from decaying. Researchers adhering to strict scientific standards have not substantiated these claims.

Related

Hierarchical structure

The hierarchical structures of some organizations are sometimes described as pyramids. This often includes sports league systems.

Game show

Pyramid is the name of a game show currently in syndication.

Novel

Pyramids is a Discworld novel by Terry Pratchett.

Album

Pyramid is a concept album by The Alan Parsons Project, released in 1978.

Magazine

Pyramid is an online magazine publishing role-playing and other game articles, published by Steve Jackson Games.

Confidence game

A pyramid scheme is a phony business, similar to a chain letter, that involves the exchange of money primarily for enrolling other people into the scheme.

External links

• The Uniform Polyhedra (http://www.mathconsult.ch/showroom/unipoly/)
• Virtual Reality Polyhedra (http://www.georgehart.com/virtual-polyhedra/vp.html) The Encyclopedia of Polyhedrada:Pyramide

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