Soccer Dad

Oz didn't give nothing to the scarecrow that he didn't already have, but he didn't teach him trig

But Oz never did give nothing to the tin man That he didn't, didn't already have

Tin Man - America

via Instapundit

Virgina Postrel writes about the glamour of the movie "The Wizard of Oz." In it, she observes that the qualities Dorothy and her companions sought were qualities that they already possessed.

Throughout the movie, Dorothy's companions demonstrate again and again that they have exactly the qualities they think they lack. None of the Wizard's tokens changes who the recipient really is or has been all along. But all provide a visible sign that transforms their owner's self-perception. "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side," the Scarecrow recites upon receiving his diploma. "Oh joy! Rapture! I've got a brain. How can I ever thank you enough?"

No hold on. What's wrong with that? It sure sounds erudite. Ah but the Scarecrow just recited a skewed version of the Pythatorean theorem, which applies to right - not isosceles - triangles. Thus his use of the word "any" is incorrect. What the Scarecrow should have said is "The sum of the square roots of the two legs of a right triangle is equal to the square root of the hypotenuse."

Had the Scarecrow made his statement correctly, then he would have been correct in the unique case of a right isosceles triangle where the angles are 90, 45, and 45 and the corresponding opposite sides have the ratio 1, .7071.... and .7071.... (Where .7071 is half the square root of two.)

So the Wizard gave the Scarecrow a diploma even though the Scarecrow didn't know his trigonometry. Talk about your grade inflation.

UPDATE: Whoops, by trying to maintain the Scarecrow's "square root" formulation, I got careless. ETBuzz e-mails:

What the Scarecrow should have said is "The sum of the square roots of the two legs of a right triangle is equal to the square root of the hypotenuse." Sorry, that is still false. If one insists on the version mentioning square roots instead of just squares, correct is "The square root of the sum of the squares of the two legs of a right triangle is equal to the hypotenuse." Shame on you!