Quote:
Originally Posted by jvang
My dad wanted me to post about my math observation; a long time ago I noticed that each successive square number is a successive odd number less than the next. So starting from 0, the first odd number is 1, which is the first square. Adding the next odd number, 3, to 1 gives 4, the second square. Add 5, get 9, add 7, get 16, etc. I’m not sure what kind of equation would describe this; it’d be trivial to code and easy to make a series describing it though. Is this a coincidental correlation or does it have some meaning?

Geometrically, think of adding one "layer" of ones to two adjacent sides of a square. I.e. for an nxn square add n to two adjacent sides and put one in the corner created. You have just added 2*n+1 to the nxn square and (n+1)*(n+1) = n*n+2*n+1.