around 800 to 500 BCE

### Vedic Fire Altar Square Diagonal

Altar construction via a special case of the Pythagorean theorem

The *Śulbasūtras* were ritual texts written by successive generations of scribes who not only copied but also commented on and extended the work of their predecessors. The *Baudhāyana-śulba-sūtra* gives a special case of the Pythagorean theorem.

The *Śulbasūtras*, no original texts of which are known to have survived, were Indian ritual texts containing geometrical content related to fire altar construction. The *Baudhāyana-śulba-sūtra*, transmitted orally as early as 800 BCE (but possibly as late as 500 BCE), stated, "The rope which is stretched across the diagonal of a square produces an area double the size of the original square" (which is a special case of the Pythagorean theorem corresponding to an isosceles right triangle) and prescribed a series of circles laid out via ropes prior to building one (of many possible shapes) of a Vedic fire altar.