When I was a little kid, I told my math teacher I had “discovered” a number that, when multiplied by the length of a side of a right triangle with equal-length legs, would give you the length of the hypotenuse. I beamed as I told her that the number was irrational, but was “around 1.414.” And I was crushed when she told me that number was √2, and that it was easily derived from the Pythagorean Theorum. Beat myself up for that one for a long time.
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