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Mahmoud Elsherif Beyond Pythagoras P.1 Pythagoras Theorem is a2+b2= c2 'a' is being the shortest side, 'b' being the middle side and 'c' being the longest side (hypotenuse) of a right angled triangle. The numbers 3,4,5 satisfy this condition and so 32+ 42=52 Because 32= 3*3=9 42=4*4=16 52=5*5=25 32+ 42=52 9+16=25 25=25 This proves Pythagoras Theorem goes with the right angled triangle with the numbers 3,4,5. Next I shall prove that Pythagoras's Theorem applies to 5,12,13 right angled triangle. 52+122=132 Because 52= 5*5=25 122= 12*12=144 132= 13*13=169 Mahmoud Elsherif Beyond Pythagoras P.2 This satisfies the Theorem of Pythagoras's goes with these numbers 5,12,13. Finally I shall prove that Pythagoras's Theorem applies to 7,24,25 right angled triangle. 72+ 242=252 Because 72= 7*7=49 242= 24*24= 576 252=25*25=625. So a2+b2=c2 72+242=252 49+576=625 This proves Pythagoras Theorem goes with the right angle triangle with the sides 7,24,25 Shortest Side Middle Side Longest Side 3 4 5 5 12 13 7 24 25 9 40 41 11 60 61 13 84 85 Mahmoud Elsherif Beyond Pythagoras P.3 I shall find the prediction of the shortest side first. 3,5,7 It goes up in 2 so in my conclusion so it will become 3,5,7,9,11,13 Now I will find the...

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