Beyond pythagoras
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The numbers 3, 4 and 5 satisfy the condition 32+42=52,
Because 32= 3x3 =9
42= 4x4 =16
52= 5x5 =25
And so 32+42=9+16=25=52
I now have to find out if the following sets of numbers satisfy a similar condition of (smallest number) 2+ (middle number) 2= (largest number) 2.
a) 5, 12, 13
52+122 = 25+144 = 169 = 132.
b) 7, 24, 25
72+242 = 49+576 = 625 +252
Here is a table containing the results:
I looked at the table and noticed that there was only a difference of 1 between the length of the middle side and the length of the longest side.
I already know that the (smallest number) 2+ (middle number) 2= (largest number) 2. So I know that there will be a connection between the numbers written above. The problem is that it is obviously not:
(Middle number) 2+ (largest number) 2= (smallest number) 2
Because, 122 + 132 = 144+169 = 313
52 = 25
The difference between 25 and 313 is 288 which is far to big, so this means that the equation I want has nothing to do with 3 sides squared. I will now try 2 sides squared.
(Middle)2 + Largest number = (smallest number)2
= 122 + 13 = 52
= 144 + 13 = 25
= 157 = 25
This does not work and neither will 132, because it is larger than 122. There is also no point in squaring the largest and the smallest or the middle number and the largest number. I will now try 1 side squared...