A recent position paper by the Karnataka government on the National Education Policy (NEP) 2020, has claimed that the Pythagoras theorem was already known to Indians from the Vedic times. A position paper is an essay that presents an arguable opinion about an issue. The goal of a position paper is to convince the audience that the opinion presented is valid, factual, and worth listening to. The position paper, which is a part of Karnataka’s submissions to the NCERT for the National Curriculum Framework, has described the Pythagoras’ theorem as ‘fake news’ and the ‘so-called Pythagoras theorem.
The Pythagoras Theorem
It is believed that the Pythagoras theorem was invented by the Greek philosopher Pythagoras who lived around 570 B.C.–490 BC. The Pythagoras theorem describes the relationship between the three sides of a right-angled triangle, in which, one of the angles is 90 degrees.
It states that a² + b² = c², where ‘a’ and ‘b’ are the two perpendicular sides, and ‘c’ is the length of the diagonal side. If any two sides of a right-angle triangle are known, the third side could be calculated with the help of the theorem. Extended to the sides of squares and rectangles and their diagonals, the equation is of immense importance in construction, navigation, and astronomy.
Conflict Over Evolution of Pythagoras Theorem
The origin of the Pythagoras theorem is disputed in many international forums. Though evidence states that the Greek philosopher Pythagoras existed, there is an element of mystery around him. It is because of the secretive nature of the school or society that he had then founded in Italy. As per the account of History of Mathematics Archive, University of St Andrews, Scotland, not much is known about his achievement is the field of mathematics as there are no writings of his own available today. Moreover now researchers claim that Pythagoras was a philosopher and not a mathematician. They are of the view that the theorem came into existence much before Pythagoras. It was in practice in India, China, and Babylonia.
The Stanford Encyclopaedia of Philosophy states that there was nothing written by Pythagoras, and that there is no detailed account of his thought written by contemporaries. It states that a number of treatises were forged in the name of Pythagoras and other Pythagoreans.
Many researchers were not comfortable associating the name of Pythagoras with the theorem. In the recent years it is connected less directly to Pythagoras, and is called the Pythagorean theorem, referring to the school of Pythagoras.
Vedic Texts of Baudhayana Sulbasutra
There are references to the theorem in the sulbasutras or the Shulba Sutras or sulbastras, which are sutra texts pertaining to the fire rituals or yajnas performed by Vedic people. They contain geometry related to fire-altar construction. The oldest of these is the Baudhayana Sulbasutra.
According to Professor K Ramasubramanian from IIT Bombay, who is an expert in history of mathematics, “in the Indian tradition, the theorem was put to use at least three centuries before Pythagoras. It is there is Baudhayana Shulba Sutras, for instance. There are many treatises that discuss the Pythagorean theorem long before Pythagoras had even existed. Baudhayana Shulba Sutra is one of the first. Shulba means measurement.”
The exact period of Baudhayana is not exactly known (like sulbasutras) as there is no direct internal evidence in this respect. The Baudhayana sutras are a group of Vedic Sanskrit texts which cover dharma, daily ritual, mathematics, and is one of the oldest Dharma-related texts of Hinduism that have survived into the modern age from the 1st-millennium BCE. Baudhayana sulbasutra is taken to be from around 800 BCE.
According to Vedic texts, the Baudhayana sulbasutra is noted for containing several early mathematical results, including an approximation of the square root of 2 and the statement of the Pythagorean theorem.
Kim Plofker, Associate Professor of Union College of New York, who has specialised in the history of Indian mathematics, stated that two of the sutras in the first chapter in the Baudhayana sulbasutra says that: “The areas [of the squares] produced separately by the length and the breadth of a rectangle together equal the area [of the square] produced by the diagonal. This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.” This equation is discussed in Baudhayana sulbasutra for the yajna rituals which involved construction of altars (vedi) and fireplaces (agni) in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles. The sulbasutras describe steps towards construction of these figures with prescribed sizes. According to Professor Dani who has done a study in the History of Mathematics stated that the Pythagorean equation is used in these procedures which involved drawing of perpendiculars. Further, the sides followed Pythagorean relation, because 3² + 4² = 5², and 5² + 12² = 13². Such combinations are called Pythagorean triples.
Earliest Evidence of Theorem
The earliest evidence around 1900-1600 BCE, is from the Old Babylonian civilisation, Mesopotamia. They called the Pythagoras’ theorem as the ‘Diagonal rule’ as that was more than a thousand years before Pythagoras.
The earliest evidence of a proof comes from a period after the sulbasutras. The oldest surviving axiomatic proof of the theorem is in the ‘Elements of Euclid’ from around 300 BCE. It is likely that many more-or-less formal geometric rationales for the Pythagorean relation were understood by many of its users before Euclid recorded his rigorous-demonstration version.
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