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MatheusMkalo
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Who First Utilized Rigorous Proofs in Mathematics?
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In summary, the conversation discusses the discovery of the formula (a+b)(a-b)=a^2-b^2. While it was possibly known to the ancient Egyptians and Babylonians, there is no proof of this. However, the Greeks most likely knew the formula and had rigorous proofs for it, unlike other civilizations.
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tiny-tim
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Welcome to PF!
Hi MatheusMkalo! Welcome to PF!
That's the same as (A + B)(A - B) = A2 - B2 …
Hi MatheusMkalo! Welcome to PF!
That's the same as (A + B)(A - B) = A2 - B2 …
I think that it was known to the ancient Greeks.
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There has reportedly been some discussion among scholars whether the Egyptians knew the formula [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
In fact, the Babylonians knew formulas like [tex]xy=\frac{(x+y)^2-(x-y)^2}{2}[/tex]. So it wouldn't seem unlikely that already the Babylonians and the Egyptians knew about [tex](a+b)(a-b)=a^2-b^2[/tex]. But, to my knowledge, there is no proof that they did.
But the Greeks almost certainly knew the formula. It seems like one of the things that Pythagoras liked to prove geometrically...
In fact, the Babylonians knew formulas like [tex]xy=\frac{(x+y)^2-(x-y)^2}{2}[/tex]. So it wouldn't seem unlikely that already the Babylonians and the Egyptians knew about [tex](a+b)(a-b)=a^2-b^2[/tex]. But, to my knowledge, there is no proof that they did.
But the Greeks almost certainly knew the formula. It seems like one of the things that Pythagoras liked to prove geometrically...
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This site: http://www.math.tamu.edu/~dallen/history/babylon/babylon.html explains that the Babylonians probably knew about the formula and used it to generate Pythagorean triples (yes, Pythagoras' theorem was also known to them!)
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coolul007
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The Greeks had rigorous proofs, while other civilizations didn't require proofs, just acceptance.
FAQ: Who First Utilized Rigorous Proofs in Mathematics?
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