Video Lecture 1: The Cord of Baudhāyana — Vedic Altar Geometry to the Modern Theorem

# Video Lecture 1: The Cord of Baudhāyana — Vedic Altar Geometry to the Modern Theorem
**Speaker:** Prof. Arvind Swaminathan | **Duration:** ~06:00 mins

### Introduction: The Heritage of Indian Geometry
Centuries before Pythagoras lived in Greece, Indian mathematician-priests called the *Sūtrakāras* constructed intricate brick fire-altars (*vedis*) like the Falcon-shaped *Śyenaciti*. To preserve sacred geometric areas under transformations, **Baudhāyana** (c. 800 BCE) recorded the earliest formal statement of this foundational theorem in the **Baudhāyana Sulba Sūtra**:
> *"dīrghasyākṣṇayā rajjuḥ pārśvamānī tiryaṅmānī ca yat pṛthag bhūte kurutastadubhayāṅ karoti"*
> *"The diagonal of a rectangle produces by itself both the areas which the longer and shorter sides produce separately."*

### 1. The Right-Angled Triangle Formulation:
In any right-angled triangle, the side opposite the $90^\circ$ right angle is the **Hypotenuse** (the longest side). The other two sides are called the legs or base and perpendicular.
$$\mathbf{a^2 + b^2 = c^2}$$
$$\mathbf{(\text{Base})^2 + (\text{Perpendicular})^2 = (\text{Hypotenuse})^2}$$

### 2. Geometric Interpretation:
The area of the square erected upon the hypotenuse is identically equal to the sum of the areas of the squares erected upon the other two sides!