I may have been a bit premature in declaring Judy the winner, but the
decision stands(if only to demonstrate the correct usage of irony). Except now she’s now been awarded second prize, but don’t worry, all the prizes are the same anyway . Who’d have thought that my little mini contest would have generated such a mathesophical discussion (or should that be philomatical? I always get those two mixed up) but then it’s as it should be as Pythagoras was a philosopher as well as a mathematician.
"Ironic you say?" Yes, ironic I say. I made up this little contest to show my gratitude and to reward one of you for voting for me. The irony is that the person who won the prize was the one person among you who definitely did not vote for me! Judy, you see, was nominated in the same category (mind you she may have voted for me, I voted for her).
And that brings us to the results:
1st Prize goes to Kila for her well thought out corollary.
2nd Prize goes to Judy for being the closest first.
3rd Prize goes to Melissa for single-handedly raising my comment count.
Honourable mention goes to Colette for being such an enigma.
If you want your prize, I need your address, email me.
And here is the explanation…There were two quotes from the Wizard of Oz, the first from the Lion and the second from the Scarecrow both from when they were given their prizes by the Wizard. On the surface, it looked like a simple quote from the movie illustrating that as a result of being awarded a prize saying I’m brainy, I actually got smarter. And that would have done if no-one actually got the real answer.
However, Kila uncovered the deeper meaning. In a perfect demonstration of just how ridiculous that concept is, she pointed out that the quote from the Scarecrow was wrong. The wording was correct, but what he said was completely wrong (which, incidentally Jenn, is why it wasn’t said by Pythagoras, you may want to hold off on lowering your goals for a bit).
To explain I’ll have to get a bit technical. In it simplest form, Pythagoras’ theorem is
and is solved by 
In English that’s "The square on the hypotenuse is equal to the sum of the squares on the other two sides."
Compare that to the Scarecrow quote which is "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining
side."
Given that we are talking about a hypotenuse, by definition we are only talking about right angled triangles, and not all isosceles triangles are right angled, in fact only those with one 90 and two 45 deg angles are. Plus, he not only mangled the theorem, it’s just plain wrong, as we need the length squared, and not the square root of the length.
Anyone still awake? Good, then have a look at this…
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