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Having a mathematical bent affords me abundant opportunities for mental amusement. For example, one day, as I was riding my bicycle in my neighborhood, I happened to notice the house-number on one of the mailboxes.
1728.
“Oh, twelve cubed,” I said to myself.
It was a few days later before I noticed the number on the mailbox next door. Ordinarily, around here, adjacent houses have numbers very close together; they may differ by two or four, but rarely much more than that. In this instance, however, the difference was considerably greater.
1716.
“Heh, look at that,” I said to my favorite audience. “Twelve less than twelve cubed.” And my favorite audience -- myself -- told me that it was an instance of . . .
And before my bicycle even got me to the next corner, I had factored out an x to get . . .
That parenthetical term is one of my favorites in algebra. It just tickles me no end that . . .
Substituting those two first-order terms in place of the second-order term, above, and rearranging them in ascending order of magnitude, I saw immediately that . . .