MHB History of Sum of Squares: Pythagoras & Beyond

AI Thread Summary
The discussion centers on the historical origins of the sum of squares of integers, with a particular focus on its connection to Pythagorean triples. Pythagoras is noted as a significant figure in this area, as his work laid the groundwork for understanding these mathematical concepts. The conversation suggests exploring additional resources, such as Wikipedia and the book "History of the Theory of Numbers," for more in-depth information. The relationship between the sum of squares and Pythagorean triples is emphasized as a key aspect of this mathematical history. Overall, the inquiry highlights the importance of historical context in understanding the development of mathematical theories.
Amer
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I would like to know some history on the subject like who is the first to think about sum of squares of integers and what he/she was thinking about. I think maybe it is related to Pythagorean triples. Thanks
 
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Amer said:
I would like to know some history on the subject like who is the first to think about sum of squares of integers and what he/she was thinking about. I think maybe it is related to Pythagorean triples. Thanks

Hi Amer,

A small bit of history about this is given in the following Wikipedia article and perhaps by following the links to the references (such as the book "History of the theory of Numbers") you might be able to learn more.

https://en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of_two_squares
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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