Which geometric ideas appear in the ancient Indian Sulbasutras?

The Sulbasutras (or "Cord-Rules"), dating from the 1st millennium BCE, served as manuals for the construction of brick fire altars used in Vedic rituals. These texts demonstrate sophisticated geometric knowledge developed by the Brahman class to ensure the precise creation of these structures.1

Key geometric ideas and techniques found in the Sulbasutras include:

• Geometric Constructions: Altar builders used ropes and stakes to perform complex tasks, such as transforming one plane figure into another of equal area.1
• Pythagorean Theorem: The texts contain early knowledge of the Pythagorean theorem, which relates the sides of a right triangle.12
• Mathematical Constants: The Sulbasutras provide values for the ratio of a circle's circumference to its diameter ($\pi$) and the ratio of the diagonal of a square to its side ($\sqrt{2}$).1

These geometric discoveries were deeply integrated into ritual life, as different altar shapes and sizes were believed to confer specific benefits, such as wealth or the attainment of heaven, upon the sponsor of the sacrifice.1