Karnataka government’s position paper on the National Education Policy has sparked a debate over the Pythagoras theorem. It has highlighted what historians and mathematicians have been claiming for a long time, that the Indians were already aware of what is called the ‘Pythagoras theorem’ since the Vedic times. The position paper, which was part of the Karnataka government’s submission to the NCERT for a national curriculum framework, referred to the Pythagoras theorem as “fake news.”
According to Madan Gopal, a former IAS officer who heads the NEP task force of the Karnataka government, the Pythagoras theorem is often debated in international forums. He informed the Indian Express that there are various theories claiming that the famous Greek philosopher did not actually exist. Gopal referred to a text called Baudhayana Sulbasutra, which refers to the Pythagoras theorem.
Was there someone called Pythagoras? Why is the theorem named after him?
According to experts, evidence suggests that Pythagoras could have existed during the period between 570 to 490 BC. However, there is a mystery surrounding him which relates to the existence of a mysterious society or school he founded in Italy. Also, his mathematical achievements are not known, because there is nothing available of his own writing at the History of Mathematics Archive, University of St Andrews, Scotland).
The Pythagoras theorem states that the relationship between the right triangle’s three sides is a function of 90 degrees.
a² + b² = c²
where a and b are the two perpendicular sides, and c is the length of the diagonal side.
If two of the three sides of the right-angled triangle are known, the Pythagoras theorem allows one to calculate the third side. This is very important in astronomy, navigation, and construction.
Reasons why Vedic mathematicians knew this before Pythagoras?
Historians have argued that there are multiple references in the Sulbasutra, which are written by Vedic Indians and refer to the rituals performed during yaganas. One of the oldest of these is the Bauddhayana Sulbasutra.
According to Shrikrishna G.Dani, a mathematics professor at the University of Mumbai, the exact period of the Baudhayana Sulbasutra is not known. It is estimated based on various factors, such as the author’s linguistic and historical backgrounds. He noted that the book could be around 800 BCE.
In academic circles, the Pythagoras theorem is known to be contained in the Baudhayana Sulbasutra. In 2008, Professor Dani wrote a paper that discussed geometry in the book. He claims that the Pythagoras theorem was not a “theorem” but rather a geometric fact.
According to Kim Plofker, an associate professor of Indian mathematics at Union College, New York, the first chapter of the Baudhayana Sulbasutra talks about two of the sutra’s main topics. She noted that the areas of the squares that are separated by the length and breadth of a rectangle are equal to the area of the square that is produced by the diagonal. This is also shown in the rectangle having sides 3, 4, 12, 15, 8, 7, and 24.
Why does the Sulbasutra have a reference to the mathematics equation?
The rituals that were performed during the yajnas involved the construction of various structures, such as fireplaces and altars in the shape of isosceles triangles, symmetric trapezia, and rectangles. The sulbasutras provided a step-by-step guide for the construction of these figures.
In his paper, Dani explained that the various procedures involved in the construction of these structures were based on the Pythagorean equation.
Did Indian mathematicians prove the equation?
According to Dani, there is no evidence that Indians or Pythagoras himself had proof. He noted that since the Greeks were unique in their concept of mathematical proof, it was only a means of carrying conviction. In other cultures, proof of a geometric statement would have been found in various ways.
Why debate on whether the Indians or Pythagoras knew the equation first is relevant
The current debate regarding the Pythagoras theorem is sparked by the position paper that was published in Karnataka. It calls the theorem fake news. Hence, an implicit claim of ownership is also needed to be established, says Professor Dani.
In response to the issue, Professor Dani stated that the concept of ‘Jagatguru syndrome’ i.e. everything that was there in India needs to be countered. He claims that the country is not going to make significant progress in modern development if it continues to believe that it is the master. Although some things are partially true, the country is not going to make significant progress in modern development if it continues to believe that it is the master, he concluded.