How did the Sulbasutras use ropes and stakes for geometric construction?

The Sulbasutras, which translate to "Cord-Rules," were collections of prose instructions used by the Brahman class to construct complex brick fire altars for ritual sacrifices.1

To achieve these precise geometric designs, altar builders utilized simple tools consisting of ropes and stakes. By manipulating these tools, they were able to perform sophisticated geometric tasks, most notably the transformation of one plane figure into another of equal area.1

These construction techniques reflect an advanced understanding of geometry, including early knowledge of the Pythagorean theorem, as well as calculations for the ratio of a circle's circumference to its diameter ($\pi$) and the ratio of a square's diagonal to its side ($\sqrt{2}$). The precision required for these altars was driven by the belief that specific shapes and sizes conferred distinct spiritual benefits upon the sponsor of the sacrifice.1