Steven Strogatz, in Opinionator:

… suppose we add all the consecutive odd numbers, starting from 1:

1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25

The sums above, remarkably, always turn out to be perfect squares. (We saw 4 and 9 in the square patterns discussed earlier, and 16 = 4 × 4, and 25 = 5 × 5.) A quick check shows that this rule keeps working for larger and larger odd numbers; it apparently holds all the way out to infinity.

Did that just blow your mind, too?

— From London.

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    Neat, huh? But there’s a pretty intuitive explanation: suppose you have a bunch of pennies arranged in a square, and you...

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