With time to kill at my job and attempting to look busy, I started writing out the squares of all the positive integers.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, got bored.
Anyway, I noticed that when you go from 16 to 25, you add another perfect square (9), and when you go from to 144 to 169, you add another perfect square (25).
Is there a pattern to this happening or does it just sort of show up every now and then?
Actually, the perfect squares you show is a pattern; you are adding the next odd integer to the previous. So you will get all the odd numbers squared eventually.
n^2 = SUM(2n-1) from 1 to n
Thank you. I received good grades in math all the way through integral calculus. However, I doubt I understood much of it.
Not really any sort of answer, but I thought I’d point out that these triplets you’re finding are indications of unit right triangles. The roots of these squares are whole numbers that fit into a[sup]2[/sup]+b[sup]2[/sup]=c[sup]2[/sup](the Pythagoren theorem). So, the can form right triangles with whole number sides, like the famous 3-4-5 triangle.
0[sup]2[/sup] and 1[sup]2[/sup] also differ by a perfect square.
I knew about 0 and 1, but I hoped that I was specific enough by saying positive integers.
Right you are. I should have paid closer attention.
Wow! I got a math thing right, sort of!
I think I should stick to explaining the niceties of illegal touching on punts in football.