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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.

Vedic Fire Altar Square Diagonal

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.

Artifact format

Unknown (lost)

Artifact origin

India

Timeline

PythagoreanTheorem timeline Babylonian Mud Wall Tablet Babylonian Inner Diagonal Tablet Babylonian Square Root of 2 Tablet Berlin Pythagorean Theorem Papyrus Plimpton 322 Vedic Fire Altar Rectangle Diagonal Vedic Fire Altar Square Diagonal Euclid's Elements Ptolemy's Quadrilateral Theorem Zhoubi Suanjing Pythagorean Theorem Proof Ibn Qurra's Pythagorean Theorem Proofs Lilāvatī of Bhāskara II

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Plofker, K. "The Śulba-Sūtras." §2.2 in Mathematics in India. Princeton, NJ: Princeton University Press, pp. 16–18, 2007.
  • Plofker, K. "The Śulbasūtras." Ch. 4, § II.b in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Ed. V. J. Katz). Princeton, NJ: Princeton University Press, pp. 387–393, 2007.
  • Sen, S. N. and Bag, A. K. The Sulbasutras. New Delhi: Indian National Science Academy, 1983.