## Pythagorean Geometry in Vedic-Era | 20 Jul 2022

**For Prelims:** Indian Ancient History, Vedic Age, Veda System

**For Mains:** Significance of Veda System, Significance of Vedic Age

### Why in News?

Recently, a position paper by the Karnataka government on the** National Education Policy (NEP) 2020** has described** Pythagoras’s theorem as “fake news”.**

- It has referred to a text called the
**Baudhayana Sulbasutra**, in which a specific shloka refers to the theorem.

### What do we need to know about Pythagoras?

**About Pythagoras:**- Evidence suggests that the
**Greek philosopher (around 570–490 BC) did exist.** - There is an element of mystery around him, largely because of the
**secretive nature of the school/society he founded in Italy.** - Relatively little is known about his mathematical achievements, because there is
**nothing today of his own writings.**

- Evidence suggests that the
**About Pythagoras Theorem:**- The Pythagoras theorem describes th
**e relationship connecting the three sides of a right triangle**(one in which one of the angles is 90°).- a
^{2}+ b^{2}= c^{2}- If any two sides of a right triangle are known, the theorem allows you to calculate the third side.

- a

- The Pythagoras theorem describes th

### How do we know that Vedic Indian Mathematicians knew this?

- There are references of Pythagoras in the
**Sulbasutras,**which are texts pertaining to**fire rituals (yajanas) performed by Vedic Indians.**- The oldest of these is the
**Baudhayana Sulbasutra.**

- The oldest of these is the
- The period of Baudhayana Sulbasutra is uncertain. It is estimated based on
**linguistic and other secondary historical considerations.**- In recent literature,
**Baudhayana Sulbasutra is taken to be from around 800 BCE.**

- In recent literature,
- Baudhayana Sulbasutra contains a
**statement of what is called Pythagoras theorem**(it was known rather as a geometric fact, and not as a ‘theorem’). - 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.

- The sulbasutras describe

### How did the Knowledge of Equation Evolve?

- The earliest evidence is from the
**Old Babylonian civilisation**(1900-1600 BCE).- They referred to it as the
**Diagonal Rule.**

- They referred to it as the
- 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.

### What are Vedas?

- The word
**Veda**signifies**knowledge**and the texts are actually about providing**mankind knowledge to conduct their entire life on earth and beyond.** - There are four major vedas:
**Rig Veda:****Oldest**existing veda among the four.- Focus is on
**worldly prosperity and natural beauty.** - Text is organised in 10 books known as
**Mandalas.** - Prominent gods mentioned in Rig Veda:
**Lord Indra, Agni, Varuna, Rudra, Aditya**etc.

**Yajur Veda:**- The name Yaju signifies
**Sacrifice**. - It concentrates on
**rites**and**mantras**of the different types of sacrifices. - Two major recensions (samhita) are:
**Shukla**, also called**Vajasaneyi Samhita.****Krishna**, also called**Taittiriya Samhita.**

- The name Yaju signifies
**Sama Veda:**- It has been named after
**Saman**(melody). - It concentrates on
**Melody**or**Songs.** - It is also called the
**Book**of**Chants.**

- It has been named after
**Atharva Veda:**- It is also known as
**Brahma Veda**and has been attributed to two rishis called**Atharban**and**Angiras.** - It concentrates on
**Peace**and**Prosperity**of human society. - Two major recensions (sakhas) are:
**Paippalada****Saunakiya**

- It is also known as