Take the tour ×  I was playing around with the squares and saw
an interesting pattern in their differences.  $0^2 = 0$        +
1  $1^2 = 1$        + 3  $2^2 = 4$        + 5  $3^2 = 9$
+ 7  $4^2 = 16$        + 9  $5^2 = 25$        + 11  $6^2 = 36$
(Also, in a very related question, which major Math Research
Journal should I contact to publish my groundbreaking find in?)
share|improve this question Could you send it to a social
science journal instead? :-) –  Simon Nickerson Jul 20 '10 at
21:42 You can also reverse your observation (which as Dan
explains is very easy to show) to get the slightly harder result
that 1+3+5+...+(2n-1) = n^2. –  Noah Snyder Jul 20 '10 at 21:42
The comment about publishing in a major math research journal is
presumably a joke, but it seems like some of the answers think
it was meant seriously.... –  Nate Eldredge Feb 4 at 22:14 add
comment  7 Answers  up vote 18 down vote accepted  alt text
Dan's algebraic justification is correct, but you may get more
intuition about why