Posted in भारत गौरव - Mera Bharat Mahan

Algebra and the Pythagoras

Union Minister for Science and Technology, Harsh Vardhan, speaking to the Indian Science Congress in Mumbai said “Algebra and the Pythagoras’ theorem both originated in India but the credit for these has gone to people from other countries” and quite predictably for secular India, has set off a storm of controversy….However there appears to be more than a grain of truth to what he says. We now know the contribution of Aryabhatta (circa 500CE) & Madhava of Irinjalakuda ( circa 1400 CE) to the unravelling of the value of Pi, Calculus, Trigonometry, Geometry & Algebra. In fact in the case of Madhava his work on the value of Pi was wrongly credited to Gottfried Leibniz of Germany for several centuries and was known as the “Leibniz Series”. In the 20th century this error has been rectified and currently is known as the “Madhava- Leibniz series”. Likewise we know that Baudhayana predated Pythagoras by about 250 years and had written in his “Sulba Sutra”the earliest known recorded statement of the Pythagorean Theorem.” The most notable of the rules (the Sulbasūtra-s do not contain any proofs of the rules which they describe, since they are sūtra-s, formulae, concise) in the Baudhāyana Sulba Sūtra says:
“dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti”.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
This appears to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.
If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.
Baudhāyana also provides a non-axiomatic demonstration using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle:
The cord which is stretched across a square produces an area double the size of the original square.

Baudhayana, (fl. c. 800 BCE) was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sutra—appendices…


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