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 Chapter 4 : Congruent Triangles Triangles in Architecture Triangles in Architecture The pyramids of Giza, towering near present-day Cairo, Egypt, are probably the most recognizable uses of triangles in architecture ever constructed in the world. Ancient Egypt's fourth dynasty (approximately 2575 B.C. to 2465 B.C.), when these pyramids were built, saw the construction of the first geometrically pure pyramids. The three pyramids of Giza are named for the kings for whom the pyramids were built. The oldest and largest of the pyramids, the Great Pyramid, was commissioned by the pharaoh Khufu, the second king of the fourth dynasty. The middle pyramid was built for Khafre, the fourth king of the fourth dynasty. It measured only 216 meters on a side, compared to the 230 meters for a side of the Great Pyramid. The southernmost, and by far the smallest of the pyramids, was built for Menkaure, Khafre's son, and the fifth king of the fourth dynasty. Its base covers less than one fourth the area covered by the Great Pyramid. Though we see the pyramids today as rough structures composed of steps formed by the massive limestone blocks, in ancient times the now-exposed yellowish limestone interior blocks were covered by smooth white outer-casing stones fit together with precise joints. The ancient Egyptians would have viewed the pyramids as true, smooth pyramids, gleaming in the harsh desert sun. Over the millennia, the pyramids have been almost completely stripped of the more desirable outer-casing stones. When the Great Pyramid was intact, its height soared to 147 meters, more than 9 meters higher than it stands today. The pyramids were constructed with amazing precision. The Great Pyramid is oriented almost exactly on the four cardinal points, the four points of a compass. Its four sides varied in length by less than 0.2 meter, even though each was over 230 meters long. The mystery of how the ancient Egyptians were able to build such monumental structures with such perfect geometric precision has still not been completely solved. Without modern surveying equipment, pulleys, or even the wheel, the Great Pyramid builders had to lift well over two million stones weighing two and a half tons each, and position each one with incredible precision in order to control the form of the rising pyramid. One of the most plausible of the modern theories of pyramid construction is that the Egyptians built a sloping embankment of brick, earth, and sand that encircled each pyramid and was built up and extended as each pyramid rose, only to be later removed. The massive stone blocks would have had to have been hauled up the ramp using sledges, rollers, and levers. You can get more information about the pyramids of Giza from The Public Broadcasting Corporation (PBS)'s NOVA Online Pyramids-The Inside Story Web site.