Talk:Diophantus II.VIII
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Questions for discussion
[edit]Diophantus II.VIII raises two interesting questions which I would like to put forward as a basis for discussion on this page.
1. Given that Diophantus lived in Alexandria , to what extent did his work draw on Egyptian sources ? We may speculate that early geodesy may have been based on Pythagorean triples in which case it would not be surprising to find that the ancient Egyptians had an algorithm for generating these and that their method is reflected in Diophantus II.VII. The same question may be asked of Ptolemy's Theorem which was crucial to the accurate calculation of early trig tables and the subsequent development of astronomy as a science. Perhaps one day the hieroglyphics of an ancient tomb or papyrus will reveal conclusively the extent of ancient Egyptian geodesic science - if indeed the construction of the Great Pyramids is not sufficient evidence in its own right.
2. When Fermat studied Diophantus II.VIII and II.IX he wrote his famous comment in the margin which later became known as ‘Fermat’s last theorem’. His claim that he had a proof of the theorem is doubted by modern Mathematicians but we must surely conclude that at very least he had a ‘substantive intuition’. What exactly did Fermat see in Diophantus II.VIII which would enable him to write his theorem so confidently ?