The ritual origin of geometry

Summary

Let us sum up the history of geometry from its beginnings in peg-and-cord constructions for circles and squares.

The circle and square were sacred figures and were studied by the priests for the same reason they studied the stars, namely, to know their gods better. The observation that the square on the diagonal of a rectangle was the sum of the squares on the sides found an immediate ritual application. Its elaboration in the sacrificial ritual gave it a dominant position in ancient thought and ensured its conservation for thousands of years. This initial elaboration took place well before 2000 B.C. By 2000 B.C., it was already old and had diffused parts of itself into Egypt and Babylonia (unless, indeed, one of these places was the homeland of the elaboration). These parts became the basis of a new development in these centers. The new, big development was the solution of the quadratic. A thousand years and more later, Greece inherited algebra from Babylonia, but its geometry has more of an Indian than a Babylonian look. It inherited geometric algebra, the problem of squaring the circle, the problem of expressing √2 rationally, and some notions of proof.