How did the ancient Egyptians use geometry?

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We know that ancient Egyptians were employing geometric concepts at least as early as 3000 BCE. Rather than using variables and mathematical symbols, the Egyptians wrote out their mathematical problems in long-hand prose or illustrated them as diagrams.

Most uses of geometry in ancient Egypt that we know about today...

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We know that ancient Egyptians were employing geometric concepts at least as early as 3000 BCE. Rather than using variables and mathematical symbols, the Egyptians wrote out their mathematical problems in long-hand prose or illustrated them as diagrams.

Most uses of geometry in ancient Egypt that we know about today were employed in the building of monumental structures, most famously the great pyramids and obelisks. The ancient Egyptians used geometric proofs to determine the size and shape of these objects before and during the construction process. They were able to calculate the area of shapes such as circles, triangles, and rectangles to a high degree of accuracy. As a result, they could determine the space required for construction as well as the quantity of building materials they would need.

The ancient Egyptians also used geometry to calculate the volume of storage structures such as granaries. For instance, the 12th century Lahun Mathematical Papyrus supplies a formula for calculating the storage capacity of a cylindrical granary. Other known documents explain how to find the storage capacity of differently shaped granaries. As a result of geometric knowledge, ancient Egyptians could plan where to store grain long before it was even harvested.

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We know that the ancient Egyptians understood geometry because of two important documents from their culture: the Rhind Papyrus (1650 BCE) and the Moscow Papyrus (1700 BCE). These documents may have been very early math textbooks: they contain geometry problems and solutions, as well as information about the Egyptian fraction system. They tell us a lot about how Egyptians used geometry, since the examples given can all be applied to daily life in those times: calculating the surface area of a basket, measuring cloth, determining the volume of different types of pyramids, etc.

The most obvious examples of the ancient Egyptians’ expertise in geometry are the pyramids. The Great Pyramid at Giza, in particular, has a nearly-perfect square base, with the four sides lined up exactly to the north, south, east, and west. Design precision like this does not happen by accident—the architects and engineers had to know how to plan it out mathematically before they started building.

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