Indian Mathematician Baudhayana Originally Discovered Pythagorean Theorem

by Sankalan Baidya
Indian Mathematician Baudhayana Originally Discovered Pythagoras Theorem

How disheartening it is to know that many of the advanced knowledge in science and mathematics and astronomy and medicine that we know today are said to be the discoveries of Europeans while the truth is that long before the west even came out of Stone Age, ancient Indian sages and scholars had not only discovered them but also put them to regular use!

The dirty game of British Imperialism not only robbed India’s wealth and culture but also belittled the highly advanced knowledge in science and philosophy. Those robbers, in an attempt to show racial supremacy even created the hoax of Aryan Race that never actually existed. It is even sadder that we Indians run for their culture while ignoring our own. It is high time that we start recognizing and respecting our own culture and it is high time that west starts giving credit for things that rightfully belongs to us.

Today we will focus of Pythagoras Theorem. Well, just like the Atomic Theory is credited to John Dalton, Pythagoras Theorem is credited to Pythagoras. The truth however is that ancient Indian sage Kanada came up with Atomic Theory over 2,600 years before John Dalton and ancient Indian mathematician and possibly a sage and an architect name Baudhayana actually gave the Pythagoras Theorem over 200 years before Pythagoras was even born.

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Who was Baudhayana?

Not much is known about Baudhayana. However, historians attach the date c. 800 BCE (or BC). Not even the exact date of death of this great mathematician is recorded. Some believe that he was not just a mathematician but in fact, he was also a priest and an architect of very high standards.

What makes Baudhayana Important?

The case of Baudhayana is one of the many examples where Greeks and other western civilizations took credit of the discoveries originally made by ancient Indians. Baudhayana in particular is the person who contributed three important things towards the advancements of mathematics:

  1. He gave us the theorem that became known as Pythagorean Theorem. Actually we should be calling it Baudhayana Theorem.
  2. He gave us the method of circling a square.
  3. He also gave us the method of finding the square root of 2.

Let us take a look at each of his contributions separately.

The Pythagorean (Baudhayana) Theorem

Baudhayana wrote what is known as Baudhayana Sulbasutra. It is one of the earliest Sulba Sutras written. Now Sulba Sutras are nothing but appendices to famous Vedas and primarily dealt with rules of altar construction. In Baudhayana Sulbasutra, there are several mathematical formulae or results that told how to precisely construct an altar. In essence, Baudhayana Sulbasutra was more like a pocket dictionary, full of formulae and results for quick references. Baudhayana essentially belonged to Yajurveda school and hence, most of his work on mathematics was primarily for ensuring that all sacrificial rituals were performed accurately.

One of the most important contributions by Baudhayana was the theorem that has been credited to Greek mathematician Pythagoras. There is an irony to this as well that we will discuss in a while.

What later became known as Pythagorean Theorem has been mentioned as a verse or a shloka in Baudhayana Sulbasutra. Here is the exact shloka followed by English interpretation:

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


dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī, cha yat pṛthagbhūte kurutastadubhayāṅ karoti.

When translated to English, it becomes:

If a rope is stretched along the diagonal’s length, the resulting area will be equal to the sum total of the area of horizontal and vertical sides taken together.

So the question is, what the heck do these horizontal and vertical sides refer to? Some people have argued that the sides refer to the sides of a rectangle and some say that they refer to the sides of a square.

Whatever the case be, if Baudhayana’s formula is restricted to a right-angled isosceles triangle, whatever is claimed by the shloka becomes to restricted. Fortunately, there is no reference to drawn to right-angled isosceles triangle and hence, the shloka lends itself to geometrical figures with unequal sides as well.

Because Baudhayana’s verse is opened, it is pretty logical to assume that the sides he referred to may be the sides of a rectangle. If so, it is actually the statement of the Pythagorean Theorem that came to existence at least 200 years before Pythagoras was even born!

It is not that Baudhayana was the only person who came up with the theorem. Later came Apastamba – another mainstream mathematician from ancient India who too provided the Pythagorean Triplet using numerical calculations.

So the next big question, why the hell is the theorem attributed to Pythagoras and not Baudhayana? That’s because Baudhayana went on to prove it by NOT using geometry but using area calculation. Later on when the Greeks started proving it, they (specifically Euclid and some others) provided geometrical proof. Since Baudhayana’s proof was not geometrical by nature, his discovery was completely ignored.

However, one thing that was interestingly suppressed that Baudhayana not only gave the proof of Pythagorean Theorem in terms of area calculation but also came up with a geometric proof using isosceles triangles. So essentially, Baudhayana gave the geometric proof and Apastamba gave the numerical proof.

Funny thing about Pythagoras?

It is clear that Pythagoras didn’t really discover the theorem. In fact it was after 300 years of Pythagoras’ so-called discovery that the theorem was credit to Pythagoras by other Greek philosophers, historians and mathematicians. Later on, many historians actually tried to find a relation between Pythagoras and Pythagorean Theorem but actually failed to find any such link but they did manage to find a relation between the theorem and Euclid, who was born several hundred years after Pythagoras.

Here is something more surprising. Many historians have actually come up with evidences that Pythagoras traveled from Greece to Egypt to India and then back to Greece. Possibly Pythagoras learned the theorem in India and took the knowledge back to Greece but hid the fact that the source of the knowledge was India.

The flimsy critics

It is not unnatural to find many critics from western world who prefer to maintain their facade of racial supremacy and egoistic western imperialism who blatantly try to discredit Baudhayana even today. They argue that what Baudhayana gave was a mere statement and that to in form of a verse or poetry or shloka and that there is no hardcore proof. Even if we are to believe that Baudhayana did not give a proof, how on earth we are supposed to believe that someone gave a formula, which forms the very basis of geometry and algebra, without really knowing the explanation or proof in details? Is that even possible? Did Einstein simply give the formula E=mC2 without giving the proof? So, these egoistic western critics are very flimsy with their criticism.

We should not forget that many (literally thousands and thousands) books and libraries were burned to ashes under British Imperialist rule of Indian subcontinent. Many of our age-old ancient knowledge has been burned down to ashes and completely destroyed by these idiots. Not just the British, India also suffered a lot during Islamic conquests. It is high time that the world looks at India with respect for producing the most advanced knowledge it science, philosophy, astronomy and medicine when the rest of the world was doomed in the darkness of ignorance.

Baudhayana’s Contribution towards Circling a Square and Pi

It was not just the Pythagorean Baudhayana Theorem that was first provided by Baudhayana. He even gave us the value of Pi (π). The Baudhayana Sulbasutra has several approximations of π that Baudhayana possibly used while constructing circular shapes.

The various approximations of π that can be found in Baudhyana Sulbasutra are:

$$\Pi =\frac { 676 }{ 225 } =3.004$$

$$\Pi =\frac { 900 }{ 289 } =3.114$$

$$\Pi =\frac { 1156 }{ 408 } =3.202$$

None of the values of π mentioned in Baudhayana Sulbasutra are accurate because the value of π is approximately 3.14159. However, the approximations that Baudhayana used wouldn’t really lead to major error during the construction of circular shapes in altars.

Baudhayana’s Contribution Towards the Square Root of 2

Interestingly Baudhayana did come up with a very accurate value of the square root of 2, which is denoted by √2. This value can be found in Baudhayana Sulbasutra Chapter 1, Verse 61. Whatever Baudhayana wrote in Sanskrit actually boils down to this symbolic representation:

$$\sqrt { 2 } =1+\frac { 1 }{ 3 } +\frac { 1 }{ \left( 3\times 4 \right) } -\frac { 1 }{ \left( 3\times 4\times 34 \right) } =\frac { 577 }{ 408 } =1.414215686$$

This value is accurate to 5 decimal places.

In case Baudhayana restricted his approximation of √2 to the following:

$$\sqrt { 2 } =1+\frac { 1 }{ 3 } +\frac { 1 }{ \left( 3\times 4 \right) }$$

In above restricted case, the error would be of the order of 0.002. This value is way more accurate than the approximations of π he provided. This is where one confusing question pops up – “why did Baudhayana need a far more accurate approximation in case of √2 compared to π?” Well, there is no one who can give us that answer.

Bottom line however is that it was Baudhayana who gave us the Pythagorean Theorem, the value of π and the square root of 2. The Greeks and other western mathematicians simply stole those discoveries, who, through the annals of history, became known as the discoverers of those concepts while Baudhayana remained discredited for his discoveries that laid down the foundations of geometry and algebra.

Sources: 1, 2, 3, 4, 5

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