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: \(1 + \frac{1}{3} + \frac{1}{3 \cdot 4} - \frac{1}{3 \cdot 4 \cdot 34} = \frac{577}{408} \approx 1.414215686\), accurate to 5 decimal places. - Circle-squaring ratio: For a circle of diameter \(d\), construct a square of side \( \frac{7}{8} d \) (approximation of \(\pi \approx 3.088\)) and a more refined method using \( \frac{13}{15} d \) (closer to \(\pi \approx 3.004\)). CONNECTION: - The √2 approximation \( \frac{577}{408} \) is a convergent of the continued Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com