Pell’s Equation and the Chakravala Method

Etymology is funny sometimes. Sometimes it tells you a lot, sometimes nothing at all. For example, the word parabola comes from the ancient Greek word for “applied.” Hyperbola comes from ὑπερβολή or “excessive” and ellipse is derived from “a deficient.” From their words, you’d almost think the Greeks weren’t fond of conic sections.

Don’t let it fool you. They loved them.

A large part of ancient Greek contributions to mathematics are based on the simplicity of taking slices of a cone. Euclid apparently wrote four books on conics…