It
was ancient Indians mathematicians who discovered 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!
Baudhayana:
It
was Baudhāyana who discovered the Pythagoras theorem. Baudhāyana listed
Pythagoras theorem in his book called Baudhāyana Śulbasûtra (800 BCE).
Incidentally, Baudhāyana Śulbasûtra is also one of the oldest books on
advanced Mathematics. The actual shloka (verse) in Baudhāyana Śulbasûtra
that describes Pythagoras theorem is given below :
“dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī, cha yatpṛthagbhUte kurutastadubhayāṅ karoti.”
Interestingly,
Baudhāyana used a rope as an example in the above shloka which 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.
Some
people might say that this is not really an actual mathematical proof
of Pythagoras theorem though and it is possible that Pythagoras provided
that missing proof. But if we look in the same Śulbasûtra, we find that
the proof of Pythagoras theorem has been provided by both Baudhāyana
and Āpastamba in the Sulba Sutras! To elaborate, the shloka is to be
translated as -
The diagonal of a rectangle produces by itself both (the areas) produced separately by its two sides.
Modern Pythagorean Theorem
The
implications of the above statement are profound because it is directly
translated into Pythagorean Theorem and it becomes evident that
Baudhāyana proved Pythagoras theorem. Since most of the later proofs
(presented by Euclid and others) are geometrical in nature, the Sulba
Sutra’s numerical proof was unfortunately ignored. Though, Baudhāyana
was not the only Indian mathematician to have provided Pythagorean
triplets and proof. Āpastamba 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. Baudhāyana
also presented geometrical proof using isosceles triangles so, to be
more accurate, we attribute the geometrical proof to Baudhāyana and
numerical (using number theory and area computation) proof to Āpastamba.
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 (not just isosceles as in some older
proofs).
One
thing that is really interesting is that Pythagoras was not credited
for this theorem till at least three centuries after! It was much later
when Cicero and other Greek philosophers/mathematicians/historians
decided to tell the world that it was Pythagoras that came up with this
theorem! How utterly ridiculous! In fact, later on many historians have
tried to prove the relation between Pythagoras theorem and Pythagoras
but have failed miserably. In fact, the only relation that the
historians have been able to trace it to is with Euclid, who again came
many centuries after Pythagoras!
This
fact itself means that they just wanted to use some of their own to
name this theorem after and discredit the much ancient Indian
mathematicians without whose contribution it could’ve been impossible to
create the very basis of algebra and geometry!
Many
historians have also presented evidence for the fact that Pythagoras
actually travelled to Egypt and then India and learned many important
mathematical theories (including Pythagoras theorem) that western world
didn’t know of back then! So, it’s very much possible that Pythagoras
learned this theorem during his visit to India but hid his source of
knowledge he went back to Greece! This would also partially explain why
Greeks were so reserved in crediting Pythagoras with this theorem!
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