Showing posts with label PYTHAGORAS. Show all posts
Showing posts with label PYTHAGORAS. Show all posts

## Sunday, March 29, 2015

### Pythagorean (Pythagoras) Theorem in Baudhayana Sulba Sutra (800 BC)

In mathematics, the Pythagorean (Pythagoras) theorem (written around 400 BC) is a relation among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
“In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).”
But in reality, this was written much earlier in ancient india by sage Baudhayana (around 800 BC).
He is noted as the author of the earliest Sulba Sūtra—appendices to the Vedas giving rules for the construction of altars—called the Baudhāyana Śulbasûtra, which contained several important mathematical results.
He is accredited with calculating the value of pi (π) before Pythagoras.
Solka in Baudhāyana Śulbasûtra that describes Pythagoras theorem is given below :
dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī, cha yatpṛthagbhUte kurutastadubhayāṅ karoti.
Baudhāyana used a rope as an example in the above sloka.
Its translation means : A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
Proof of Pythagoras theorem has been provided by both Baudhāyana and Āpastamba in their Sulba Sutras.
Though, Baudhāyana was not the only Indian mathematician to have provided Pythagorean triplets and proof. Āpastamba also provided the proof for Pythagoras theorem, which is numerical in nature and unfortunately, Pythagoras was wrongly credited by Cicero and early Greek mathematicians for this theorem.
Also, another ancient Indian mathematician called Bhaskara later provided a unique geometrical proof as well as numerical which is known for the fact that it’s truly generalized and works for all sorts of triangles and is not incongruent.
citation-www.booksfact.com

## Sunday, January 4, 2015

### PYTHAGORAS STOLE BUDDHAYAN FORMULA

THE REAL PYTHAGORAS
Recently, at the inauguration of the 102nd edition of the Indian Science Congress, union minister of science and technology, Dr Harsh Vardhan, mentioned that it was our scientists, from ancient India who discovered the Pythagoras theorem and we have always shared our knowledge with the whole world selflessly. This is something that each of us should be proud of. Right ? To my utter shock, many people including several scientists, objected and mocked the comment.
But Dr Harsh Vardhan is absolutely right !!
Ancient Indian mathematicians discovered the Pythagoras theorem. This might come as a surprise to many, but it’s true that Pythagoras theorem was known much before Pythagoras and it was Indians who actually discovered it at least 1000 years before Pythagoras was born!
It was Baudhayana who discovered the Pythagoras theorem. Baudhayana listed Pythagoras theorem in his book called Shulba Sutra (800 BCE). It is also one of the oldest books on advanced Mathematics. The word 'Shulba' in Sanskrit means rope or cord. Hence Shulba Sutra was a book of geometry. The actual shloka (verse) in Baudhayana Shulba Sutra that describes Pythagoras theorem is :
dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
The above shloka can be translated as – A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.As you see, it becomes clear that this is perhaps the most intuitive way of understanding and visualizing Pythagoras theorem (and geometry in general) and Baudhāyana seems to have simplified the process of learning by encapsulating the mathematical result in a simple shloka in a layman’s language.
Though, Baudhayana was not the only Indian mathematician to have provided Pythagorean triplets and proof. Apastamba also provided the proof for Pythagoras theorem, which again is numerical in nature but again unfortunately this vital contribution has been ignored and Pythagoras was wrongly credited by Cicero and early Greek
mathematicians for this theorem. Baudhayana presented geometrical proof using isosceles triangles so, to be more accurate, we attribute the geometrical proof to Baudhayana and numerical (using number theory and area computation) proof to Apastamba.
Apart from the two, another ancient Indian mathematician called Bhaskara later provided a unique geometrical as well as numerical proof of the Pythagoras theorem, which works for all types of triangles (not just isosceles as in some older proofs).
Mathematicians and scientists from all over the world are now accknowleging and accepting the accompliments of ancient Indians in the fields of maths and science.
Now its our turn to do the same !!
Poonam Patil Kalra