1=1^2 1+3=2^2 1+3+5=3^2 1+3+5+7=4^2
Who's is this theorem, who is the first to realyse this? Nicomah, Aristotel, Archimedes? I need to know for sure and fast plz. thanx
1=1^2 1+3=2^2 1+3+5=3^2 1+3+5+7=4^2 Who's is this theorem, who is the first to realyse this? Nicomah, Aristotel, Archimedes? I need to know for sure and fast plz. thanx 


This question appears to be offtopic. The users who voted to close gave this specific reason:
According to L. E. Dickson's History of the theory of numbers, vol. 2, ch. 1, this goes back to Pythagoras (570501 BC) Later: Ah... Browsing that book is always fun. «N. Beguelin made a puerile illogical attempt to prove that every number is a sum of three triangular numbers». Poor guy: Dickson does not treat him with any kindness at all... 


I doubt this question has a definitive answer, but Fibonacci discusses this in Liber quadratorum:
My source: http://www.gapsystem.org/~history/Biographies/Fibonacci.html 


The original source, attributing this theorem to the early pythagoreans is Theon of Smyrna. Eduard Hiller: Expositio Rerum Mathematicarum ad legendum Platonem utilium. Rec. Theon Smyrnaeus, reprinted by Teubner, Stuttgart, 1995. Further Aristoteles writes, with reference to the early pythagoreans too: "the gnomons are placed round the one" explaining in a somewhat dark manner the geometric aspect of the sum of odd numbers, placed around the 1 Physics, book 3, chapter 4 as sketched in the answer by Stefan . So there is no chance to find an individual name of the first inventor other than Pythagoras himself. But it is not clear what he really did. No documents of his are left. (Nicomachus, Aristotle, and Archimedes definitively lived too late.) 


Achemides from what I recall but my citations are buried in old discrete math books. 

