Geometry

While the origins of geometry are likely to remain a matter of pure speculation, the elaborate written cultures of ancient Egypt and Babylon provide a wealth of information about the uses of geometry. Area and volume measurements abound in work connected with taxation, the provision of cities, and large-scale building works. Sometimes the Babylonians' evidence (which survives because they wrote on durable clay tablets) spills over into purer matters, and reveals methods for finding the areas of circles, and an impressive calculation of the length of the diagonal of a unit square. The so-called Pythagorean Theorem for right-angled triangles was used to find sides and diagonals of rectangles, and approximate methods for finding square roots. Other tablets display a cut-and-paste method for dealing with questions that could be formulated as quadratic equations—the origins of the method of completing the square—that depends for its validity on a certain amount of elementary geometry.