How were fire altars connected to the development of geometry in Vedic India?

In Vedic India, the development of geometry was deeply intertwined with the construction of brick fire altars used for ritual sacrifices. The primary evidence for this mathematical activity is found in the Sulbasutras (or "Cord-Rules"), which are 1st-millennium BCE texts that provided precise instructions for building these altars.1

Because different altar shapes and sizes were believed to confer specific spiritual or material benefits—such as wealth or the attainment of heaven—priestly functionaries (the Brahman class) required sophisticated geometric techniques to construct them accurately. Using simple tools like ropes and stakes, these builders developed advanced methods, including:1

• Geometric Transformations: The ability to transform one plane figure into another of equal area.1
• Fundamental Principles: Knowledge of the Pythagorean theorem, as well as values for the ratio of a circle's circumference to its diameter ($\pi$) and the ratio of a square's diagonal to its side ($\sqrt{2}$).1

It remains a subject of historical interest whether these ritual requirements directly inspired the discovery of these geometric principles, or if the beauty of the geometry itself led to its integration into sacred ritual practice.1