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Context

A Position paper by the **Karnataka government** on the National Education Policy (NEP) 2020 has revived discussion that what we call the **Pythagoras theorem** was already known to Indians from the **Vedic times.**

Background

**Historical Background**

- The Pythagoras theorem describes the relationship connecting the three sides of a
**right triangle**(one in which one of the angles is 90°). - There are similar references in the sulbasutras, which are texts pertaining to
**fire rituals**(yajnas) performed by Vedic Indians. The oldest of these is the ‘**Baudhayana Sulbasutra’.** - Baudhayana Sulbasutra contains a statement of what is called Pythagoras theorem.
- The earliest evidence of a proof comes from a period after the sulbasutras.
- The oldest surviving axiomatic proof of the theorem is in the
**Elements of Euclid**from around**300 BCE.** - It was mentioned in a paper describing geometry in the sulbasutras in ‘
**Studies in History of Mathematics**, Proceedings of Chennai Seminar’ in

**What is the evidence that Sulbasutra contains?**

- In the first chapter in the Baudhayana Sulbasutra contains, the (areas of the squares) produced separately by the length and the breadth of a rectangle together equal the area (of the square) produced by the diagonal.
- This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.
**Uses:**- The
**yajna rituals**involved construction of altars (vedi) and fireplaces (agni) in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles. - The sulbasutras describe steps towards construction of these figures with prescribed sizes.

**What Pythagoras theorem says?**

- The Pythagoras theorem describes the relationship connecting the
**three sides**of a right triangle (one in which one of the angles is 90°):**a² + b² = c²,**where a and b are the two perpendicular sides, and c is the length of the diagonal side. - If any two sides of a right triangle are known, the theorem allows you to calculate the third side.
- Extended to the sides of squares and rectangles and their diagonals, the equation is of immense importance in
**construction, navigation and astronomy.**

**What is the similarity between Sulbasutra’s equation and Pythagoras?**

- The Pythagorean equation comes into play in these procedures, which involve drawing perpendiculars.
- These perpendiculars were based on triangles whose sides were in the ratio 3:4:5 or 5:12:13.
- These sides follow the Pythagorean relation, because 3² + 4² = 5², and 5² + 12² = 13². Such combinations are called
**Pythagorean triples.**

**Did Indian mathematicians prove the equation?**

- The idea of a mathematical proof based on an axiomatic structure is
**unique to the Greeks**. - Thus in respect of the other cultures, ‘proof’ of a geometrical statement only meant some means of various cultures like one India has in its
**Vedic times.**

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