I was bored in geometry today, so I played with squared numbers a little.

0^2 + 1^2 = 1 | 1*5=5
1^2 + 2^2 = 5 | 5*2.6=13
2^2 + 3^2 = 13 | 13*1.923076923=25
3^2 + 4^2 = 25 | 25*1.64=41
4^2 + 5^2 = 41 | 41*1.487804878=61
5^2 + 6^2 = 61 | 61*1.393442623=85
6^2 + 7^2 = 85 | 85*1.329411765=113
7^2 + 8^2 = 113 | 113*1.283185841=145
8^2 + 9^2 = 145 | 145*1.2488275862=181
9^2 + 10^2 = 181

100^2 + 101^2 = 20201
101^2 + 102^2 = 20605
20605 / 20201 = 1.01999901

181 / 5 = 36.2
181 / 13 = 13.92307692
36.2 / 13.92307692 = 2.60000001

The numbers multiplied by the product of the squared numbers to equal the next product of squared numbers becomes smaller and smaller. Can this trend (or whatever it's called) stop, or does it have no end? [edit] The multiplier never becomes smaller than 1?

I thought it was neat.:whistling: