Sulba Sutras: Ancient Indian Geometry with Pythagorean Theorem and Circle-Squaring — E8 Intelligence Research

FINDING: The Sulba Sutras contain explicit geometric constructions for ritual altars, including the earliest known statement of the Pythagorean theorem (Baudhayana), approximations for √2, and methods for squaring the circle and transforming areas. MATH: - Pythagorean theorem: *dīrghasyākṣṇayā rajjuḥ pārśvamānī tiryaḍ mānī ca yat pṛthag bhūte kurutastadubhayaṃ saṃkaroti* — "The diagonal of a rectangle produces both areas which its sides produce separately." This is equivalent to \(a^2 + b^2 = c^2\). - √2 approximation: \(1 + 1/3 + 1/3 · 4 - 1/3 · 4 · 34 = 577/408 ≈ 1.414215686\), accurate to 5 decimal places. - Circle-squaring ratio: For a circle of diameter \(d\), construct a square of side \( 7/8 d \) (approximation of \(π ≈ 3.088\)) and a more refined method using \( 13/15 d \) (closer to \(π ≈ 3.004\)). CONNECTION: - The √2 approximation \( 577/408 \) is a convergent of the continued Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com