Thread by @ancient_bharat

Do you know?

Baudhayana (800 BC) – The great Indian Mathematician gave Pythagoras Theorem at least 500 years before Pythagoras was even born.

Baudhayana is among one of the first to discover value of π about 2800 years ago!

Also gave method of finding square root of 2.
#Thread

दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

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

Baudhāyana seems to have simplified the process of learning by encapsulating mathematical result in a simple shloka in a layman’s language.

As you see,it becomes clear that this is perhaps the most innovative way of understanding & visualizing theorem (And geometry in general).

The Baudhayana sūtras

Baudhayana is credited with significant contributions towards the advancements in mathematics. The most prominent among them are as follows

1. Baudhayana/Pythagoras theorem
2. Value of π
3. Circling a square.
4. The method of finding the square root of 2.

The method of finding the square root of 2.

Baudhayana gives the length of the diagonal of a square in terms of its sides.

The measure is to be increased by 3rd & by 4th decreased by the 34th.
That is it’s diagonal approximately.
That is 1.414216,which is correct to 5 decimals.

Baudhāyana (elaborated in Āpastamba Sulbasūtra i.6)
gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2.

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayettac caturthenātmacatustriṃśonena saviśeṣaḥ

Sama – Square;

Dvikarani – Diagonal (dividing the square into two), or Root of Two

Pramanam – Unit measure;

tṛtīyena vardhayet – increased by a 3rd

Tat caturtena (vardhayet) – that itself increased by a 4th, Atma – itself;

Caturtrimsah savisesah – is in excess by 34th part

It can be concluded without a doubt that there is a lot of emphasis on rectangles and squares in Baudhayana’s works.
This could be due to specific Yajna Bhumika’s, the altar on which rituals were conducted, for fire-related offerings.

Circling a square.
Baudhayana was able to construct a circle almost equal in area to a square &vice versa
These procedures are described in his sutras (I-58&I-59)

Possibly in his quest to construct circular altars,he constructed 2 circles circumscribing the 2 squares shown below

Now,just as the areas of the squares, he realised that the inner circle should be exactly half of the bigger circle in area.

He knew that the area of the circle is proportional to the square of its radius and the above construction proves the same.

By the same logic, just as the perimeters of the 2 squares, the perimeter of the outer circle should also be √2 times the perimeter of the inner circle.

This proves the known fact that the perimeter of the circle is proportional to its radius.

This led to an important observation by Baudhayana.

That the areas and perimeters of many regular polygons, including the squares above, could be related to each other just as the case of circles.

source :
1. books.google.co.in/books?id=DHvTh…

2. sacred-texts.com/hin/sbe14/sbe1…

3. S. Balachandra Rao, Indian Mathematics and Astronomy: Some Landmarks. Jnana Deep Publications, Bangalore, 1998. ISBN 81-900962-0-6

books.google.co.in/books?id=DHvTh…

4. Vincent J. Katz. A History of Mathematics: An Introduction, 2nd Ed. Addison-Wesley, 1998. ISBN 0-321-01618-1

5. mathshistory.st-andrews.ac.uk/Biographies/Ba…

6. mathshistory.st-andrews.ac.uk/HistTopics/Ind…

7. mathshistory.st-andrews.ac.uk/Projects/Pearc…

8. B.B. Dutta."The Science of the Shulba".

mathshistory.st-andrews.ac.uk/HistTopics/Ind…