Sulba Sutras: Ancient Vedic Geometry with Pythagorean Theorem and Irrational Approximations — E8 Intelligence Research

Abstract

FINDING: Sulba Sutras contain explicit geometric constructions for ritual altars, including early forms of the Pythagorean theorem, square-circle equivalences, and irrational approximations. MATH: - Baudhayana Sulba Sutra (c. 800 BCE): *dīrghachatursrasya akṣṇayā rajjuḥ pārśvamānī tiryagmānī ca yat pṛthagbhūte kurutastadubhayaṃ karoti* — "The diagonal of a rectangle produces both areas which its length and breadth produce separately." This is the Pythagorean theorem: \( a^2 + b^2 = c^2 \). - Approximation for √2: *samasya dvikaraṇī pramāṇaṃ tṛtīyena vardhayet tac caturthenātmacatustriṃśonena* — "Increase the side length by its third, then by its fourth, subtract the 34th part." This yields: \( 1 + \frac{1}{3} + \frac{1}{3 \cdot 4} - \frac{1}{3 \cdot 4 \cdot 34} = \frac{577}{408} \approx 1.414215686 \), accurate to 5 decimal places (true √2 ≈ 1.414213562). - Circle-squaring construction: *caturasraṃ maṇḍalaṃ nikṣipet* — "Transform a square into a circle of equal area." Implicit r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com