Vedic Rituals and Fire Altars

Śulba-sūtras and Ritual Geometry

• The Śulba-sūtras are ancient Indian ritual practice texts that describe the construction of fire altars of specific sizes and shapes for different types of sacrifices.
• The altars were built using baked bricks of prescribed numbers and dimensions, with the footprint laid out on leveled ground using measuring cords of various lengths.
• The Śulba-sūtras provide terse, cryptic instructions, often in the form of verses, for constructing the altars.
• The texts describe area-preserving transformations of plane figures, including squares, rectangles, triangles, trapezia, rhomboids, and circles.
• The rituals required the transformation of one shape into another of the same size, involving geometric formulas and constants.

Authors and Historical Context

• The best-known Śulba-sūtras are attributed to authors Baudhāyana, Mānava, Āpastamba, and Kātyāyana, in approximately chronological order.
• The texts are ascribed to various ancient sages, but little is known about them beyond their names.
• The historical context of the Śulba-sūtras is unclear, with no contemporary texts that can answer questions about their origins.

Examples of Ritual Geometry

• In one ritual, a smaller altar is required for a sacrifice to Indra, with identical proportions to the Great Altar but only one-third of its area.
• The ritual requires replacing the linear unit with its "one-third-maker" or using smaller multiples of the tripler to achieve the desired shape.
• The altar dimensions are specified in terms of the double-pace and its tripler, with precise instructions for constructing the altar.