A pyramid is typically a five-sided three-dimensional object, though four-sided is not uncommon. The majority of the sides are triangular in a five-sided pyramid. One angle from each of these triangles meets at a point (this is considered "top"). The fifth side is a square. Four-sided pyramids have triangles for all four sides. The regular tetrahedron, a Platonic solid with four faces, takes the shape of a pyramid with equilateral triangles for its base and sides.
There are some rather famous pyramids in Egypt. They are huge stone structures that were built (by flesh-and-blood human beings who were mostly not slaves and certainly not extraterrestrials) as the tombs for ancient pharaohs.
 Pyramid woo
Some people believe pyramidal structures have special powers, for healing, calming, focusing spiritual energies or sharpening razor blades. You can even buy pyramidal frames to wear on your head. While whatever someone thinks helps them meditate is fine, they should keep in mind that there is no basis in reality for these beliefs.
Some woo merchants ascribe the building of ancient pyramid structures by geographically isolated peoples as being evidence for the mystical nature of pyramids. Erich von Däniken belongs to the select group of wingnuts claiming that the pyramids (Egyptian and Mesoamerican) were built by outsiders, such as Atlanteans or aliens.
Another common rationale for pyramids having been built with the help of aliens is: How could an ancient civilization have built something so grand with such limited tools? Problem is, that line of thought falls into a gross underestimation of human ingenuity – we've achieved more sophisticated feats of engineering having developed the right tools, but any human achievement is staggering and improbable if you don't consider the history of its development.
 Why did geographically separated cultures build pyramids?
At a quick glance, it may seem odd that cultures as diverse as the Mayans and the Egyptians would build oddly similar structures. Both cultures were inspired by religion, but the usage and construction techniques varied.
 Physics determines the stability of a structure
Ancient peoples chose the approximate pyramid shape because it was the one most suitable for the building of large structures, based on materials available at the time. Go in to your garden and try to build a structure made of earth as high as your waist. The easiest way to do this is to build a mound, or something similar to a pyramid. We can determine this with a few hours spent digging in the garden, so is it unrealistic to expect that ancient engineers could achieve a similar realization without requiring assistance from aliens or Atlanteans?
A comparison of Mesoamerican and Egyptian pyramids reveals clear differences in their respective designs. Mesoamerican cultures normally built step-pyramids, where the tiers are clearly visible. Egyptian pyramid design began with step pyramids, transitioning to forms that had a smooth finish by addition of a limestone casing. The underlying steps are visible where the limestone casing has eroded or been removed, as has happened to the Pyramid of Cheops.
 Evolution of the pyramid
As is the case with biological evolution, similar traits can independently evolve. The appearance of the wheel could be ascribed to Atlanteans seeding geographically isolated cultures with the invention, or one could reason that a round shape is the most efficient choice for the construction of wheels. Given that the ancient engineers were facing the same physical constraints, it's reasonable to assume that they may converge on a similar solution.
Pyramids did not simply appear in their final forms. A study of the pyramids of Egypt and Africa reveals a clear progression from the mastaba, typically single-tiered structures, to the Pyramid of Cheops -- and the intervening structures. Early pyramids, such as the Step Pyramid of Djoser[wp], resemble a series of mastaba stacked on top of each other, with each tier being smaller than the one below it. Hey, isn't it odd that the tallest and most stable hills and mountains tend to have a relatively smooth gradient?
The development of pyramid building techniques is comparable to the progression of skyscrapers. The Empire State Building did not simply spring in to existence. Prior to its completion, the Eiffel Tower was the tallest human-made construction in the world. There is ample evidence of this progression, right back to the crude buildings of pre-history.
 Differing motives and uses of pyramids
The Egyptians built their pyramids as tombs, since their beliefs required that the body be preserved in order to achieve immortality. This is why pharaohs went to great efforts to protect their tombs. Mesoamerican pyramids were predominantly built as places of worship and ritual. Mesoamerican pyramids, unlike Egyptian pyramids, were commonly built with a temple complex at the summit.
 See also
- ↑ Czech patent for pyramid razor-blade sharpener (1959)
- ↑ Wikipedia entry on "Pyramid Power"
- ↑ http://www.shambhalahealingtools.com/Buddha_Maitreya_Head_Pyramids_Pyramid_Grids_s/20.htm A snip at $175!
- ↑ Ancient astronauts: Builders of ancient monuments?
- ↑ The evolution of the Egyptian pyramid
- ↑ Wikipedia article on Mesoamerican pyramids
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