Pythagoras Theorem known well before time of Pythagoras - Baudhayana theorem and Babylonians had Pythagorean triplets
Pythagoras Theorem was known centuries before - Baudhayana theorem. Expressed in Baudhayana Śulbasûtra. Also Pythagorean triplets were used by Babylonians well before Pythagoras
Pythagoras lived in the time period of about 570-490 BCE.
Baudhayana is dated to be around 800 BCE.
The actual shloka (verse) in Baudhāyana Śulbasûtra that describes Pythagoras theorem is given below :
दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥
dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.[7]
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).
“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius […] The tablet not only contains the world's oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”
Dr. Mansfield said in a video about the research results that the 60-base system allowed the Babylonians to have more accurate results than the modern use of base 10. The different approach used by the Babylonians to arithmetic and geometry may have “possible practical applications in surveying, computer graphics and education.” It is believed the tablet was created in the ancient Sumerian city of Larsa sometime between 1822 and 1762 BC; but Plimpton 322 got its name from a New York publisher named George Plimpton, who donated it to Columbia University in the 1930s. Researchers have been enamored with the artifact ever since. As Dr. Mansfield says , “Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realized it contains a special pattern of numbers called Pythagorean triples.”
Of course this doesn't necessarily prove they presented it in the form of a theorem or proved it. But its clear knew the use of Pythagorean triplets for practical purposes.
Another article on Babylonian maths related to this:
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