Ancient (Non-Greek) Geometry General • Geometry literally means “Earth measurement”. • Societies considered here are Egyptian, Babylonian, Indian, and Chinese. Miscellaneous • A lot of apparent interest in unit conversion problems. • Double-diFerence method of surveying common in China, and India. ◦ How does it work? ◦ Why wouldn’t they use something simpler? • Egyptians had right formula for a frustum of a pyramid, unlike other ancient civilizations. (It is not average base area times height.) • Babylonian geometry very algebraic. Early sliding ladder problem!: “A ladder of length 30 stands against a wall; the question is, how far will the lower end move out from the wall if the upper end slips down a distance of 6 units?” • Was geometry purely a tool for these ancient civilizations? What about the strange algebra problems connected with geometry in Mesopotamia? Trigonometry
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