Baudhayana The Mathematician behind the Pythagoras Theorem

Hi, Today we explore the life history of Baudhayana, one of the earliest known mathematicians who mentioned the Pythagorean theorem long before Pythagoras himself! Let’s understand more about him through this article.

Who is Baudhayana?

Baudhayana was an Indian Mathematician who was born in 800 BC and died in 740 BC. He was a Vedic brahmin priest. He is said to be the original founder of Pythagoras’s Theorem.

Baudhāyana discovered Pythagoras at least 1000 years before Pythagoras was born. The Sulba Sutras was written by Baudhayana long before the mathematical term “Pi” was officially named and long before the Pythagorean Theorem was widely recognized in Greece. 

He was amongst the first-ever Indian Mathematicians who calculated the value of pi. According to Baudhayana, the approximate value of pi was 3. In his Sulba Sutra, he used different values of pi for different geometric constructions, especially when drawing circular shapes. 

Some of these values were surprisingly close to the actual value of pi that we use today, though they were mainly used to ensure the correct shape and size of altars. Later, in 499 AD, the famous Indian mathematician Aryabhatta calculated a much more accurate value of pi—3.1416.

This means Indian scholars like Baudhayana were using these mathematical ideas well before they were formally named or became popular in Western mathematics.

Baudhayana theorem

A shloka from the Śulbasûtra is proof that he had the concept of Pythagoras theorem in his mind even before the Pythagoras was actually made:

“dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī, cha yatpṛthagbhUte kurutastadubhayāṅkaroti.”

It means “A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.”

also says that if x and y are two sides and z is the hypotenuse, such that ‘x’ is divisible by 4.

Then, z = (x – x/8) + y/2. (In all Pythagorean triplets, one of the two shorter sides should be at least be divisible by 4)

When constructing circular shapes, Bodhayana uses different approximations for π. Constructions are given which are equivalent to taking π equal to 676/225 (where 676/225 = 3.004), to 1156/361 (where 1156/361 = 3.202), 900/289 (where 900/289 = 3.114).

Baudhayana Other Notable Contribution:

Bodhayana even tried to find a circle whose area is the same as that of a square.

“Draw half its diagonal about the centre towards the East-West line; then describe a circle together with a third part of that which lies outside the square”.

Bodhayana even figured out:

1. Diagonals of a rhombus bisect at right angles, 
2. Diagonals of a rectangle bisect each other, 
3. The midpoints of a rectangle joined forms a rhombus whose area is half the rectangle, etc.
4. The area of a square formed by joining the middle points of a square is half of the original.

He was just like the other Mathematicians who were born around 800 BC like Aryabhatta, Bhaskara, Varahamihira, Mahavira, Brahmagupta.

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Baudhayana Books: Sulbasutras

He is the author of Sulbasutras. Śulbasûtra is one of the oldest books on advanced Mathematics. Sulbasutras are all about rules for religious rites. This book contains several important mathematical results. 

The Shulba Sutras belong to a larger group of texts known as the Shrauta Sutras, which are considered extensions or appendices of the Vedas. These texts are among the very few sources that give us insight into Indian mathematics during the Vedic era.

In Vedic traditions, different shapes of fire altars (called Vedis) were believed to attract different blessings from the gods. Among all the Shulba Sutras, four are especially important for their mathematical content. These were written by Baudhayana, Manava, Apastamba, and Katyayana.

The language used in these texts is a later form of Vedic Sanskrit, suggesting that they were written sometime during the first millennium BCE. The oldest of them is believed to be Baudhayana’s Sutra, which was likely composed between 800 BCE and 500 BCE.

Baudhyana’s book contains 3 chapters. In all these 3 chapters, he has written how he has calculated the value of pi, calculated the square root of 2, and circled the area of the square and worked on Pythagoras theorem.

This book has geometric solutions of a linear equation in a single unknown. Quadratic equations of the forms ax^{2} = cax2=c and ax^{2} + bx = cax2+bx=c. Approximate value for √2 is given in Chapter 1 verse 61 of this book. According to him, the value for √2 is 1 + 1/3 + 1/(3×4) – 1/(3×4×34)= 577/408 which is 1.414215686 which is correct up to five decimal places.

These sutras written in Sanskrit cover topics based on dharma, mathematics, daily ritual, etc.

The Baudhayana sutras consist of six texts:

1. the Śulbasûtra in 3 Adhyāyas.
2. the Dvaidhasûtra in 4 Praśnas,
3. the Dharmasûtra in 4 Praśnas 
4. the Śrautasûtra, probably in 19 Praśnas
5. the Grihyasutra in 4 Praśnas,
6. the Karmāntasûtra in 20 Adhyāyas

The Baudhāyana Śulbasûtra contains several early mathematical results, like the square root of 2 and the Pythagorean theorem.

Contributions of Baudhayana in Mathematics

1. He has done research on Circle, Square, Rectangle, Triangle.
2. Discovered π to some degree of precision.
3. He is the earliest founder of Pythagoras’s Theorem.
4. He judged the square root of 2 to five decimal places of accuracy.

Interesting facts about Baudhayana

1. He was a priest and a brahmin. He used to perform Yogas with other Sages.
2. He had mentioned about the Pythagoras theorem 1000 years before the name was actually coined.
3. His book, Sulbasutras is one of the oldest mathematical books..

Frequently Asked Questions

1. Did Baudhayana discover pi?

Baudhayana did not exactly discover pi, but he gave one of the earliest known approximations of its value in his Sulba Sutra. He used different values of pi for different types of altar constructions, with one approximation being 3.

2. What is Baudhayana famous for?

Baudhayana is best known for writing the Sulba Sutras, where he explained mathematical ideas needed for religious rituals, especially for building fire altars. He is also known for mentioning a version of what we now call the Pythagorean Theorem, long before Pythagoras.

3. What did Baudhayana compose?

He composed the Baudhayana Sutras, which include the Sulba Sutra. These texts focus on rules for performing rituals and include mathematical instructions for constructing altars with precise shapes and measurements.

4. Who is the father of geometry in India?

While there isn’t a single official title, Baudhayana is often considered one of the earliest contributors to geometry in India due to his work in the Sulba Sutras, which contain many geometric concepts.

5. Who first proved pi?

The value of pi was not “proven” in ancient times, but early approximations were made by mathematicians like Baudhayana and later Aryabhatta. Aryabhatta, in 499 AD, gave a much more accurate value of pi as 3.1416.6. Who invented Baudhayana’s theorem?

The theorem known as Baudhayana’s theorem is actually an early form of the Pythagorean Theorem. Baudhayana described it in his Sulba Sutra centuries before Pythagoras, which shows that Indian scholars were aware of this geometric principle long ago