So far most everyone here has screwed up the solution to this quandary at least partially. Once and for all, here is the correct version of the line in the film, word for word. The Scarecrow actually says: "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side". Please do not doubt this transcription. It has been confirmed several times personally by me using a DVD copy of the film. According to Ray Bolger himself, he did not slip up. He delivered the line as it appeared in the screenplay supplied to him (find yourself a copy and confirm this much for yourself). His job was to act according to the screenplay and that is precisely what he did. Furthermore, nobody associated with the production of The Wizard of Oz ever claimed that this correctly delivered line was mathematically true. It clearly is not. The closest mathematically truthful match to this correctly delivered screenplay line would be: The sum of the "squares" (rather than "square roots") of "the shortest" (rather than "any") two sides of "a right angle" (rather than "an isosceles") triangle is equal to the "square" (rather than "square root") of the remaining side. This is NOT the triangle inequalities theorem, rather it appears as merely a failed attempt at a watered down version of "Pythagoras' Theorem". Those are the absolute facts. Now we have the variables. According to at least one interview with Mr. Bolger himself, the mathematically incorrect nature of the screenplay line was NOT intentional. He and his family members have clarified in the past that it was a blunder by the otherwise well educated screenwriters whose math skills weren't on par with their literal ones. I suppose Mr. Bolger may have had more than one opinion/interview response on the matter over the years. Someone with interview footage of him on file might possibly have an argument. Anyone else should stick to giving their opinion rather than pretending to be factual.
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Of course what the scarecrow says is gibberish. The point of the story was that by the time the Scarecrow, the Tin Man and the Lion got to the Wizard, they had already demonstrated that they possessed what they thought they were lacking anyway. Maybe the Scarecrow is still lousy at geometry :) But he was smart enough to think to bring the chandelier down on the guards and save Dorothy's life. Same kind of situation with the others. Thus, the gift from the wizard didn't make the Scarecrow any smarter at all, it was just a confidence-booster.
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This was parodied once on "The Simpsons" (can't recall which episode)
when Homer put on Henry Kissinger's forgotten glasses in the washroom. Just like the scarecrow, he points to his temple & quickly & confidently recites the the theorem, but says "isosceles triangle" by mistake. A voice in the stall corrects him: "That's a right triangle you idiot!" resulting in a "D'oh!"
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The line goes like this, "The sum of the square roots of any two sides of an iscoceles triangle, is equal to the square root of the remaining side." If you know anything about math, you know that this theorem pertains to right triangles not iscoceles. It is not a slip-up. I performed this role a couple of years ago and that is the line in the script. It is like this to show that the scarecrow could think, he just didn't always make sense.
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It's actually not correct for a right triangle either. He says the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side, when it actually is the squares, not square roots. The Pythagoreom Theorem is a squared + b squared = c squared. Plus, it was a deliberate joke on the part of the filmmakers to show that intelligence is more than just being able to memorize a formula.
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Yeah, she IS dreaming, and also, if this were SUPPOSED to be logical, neither the Scarecrow or the Tinman would even exist since you can't function without a heart or a brain. So don't overanalyze this, ok?
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a squared plus b squared equals c squared.
a and b are the two shorter sides of a right triangle.
"The sum of the squares of the two shorter sides of a right triangle equals the square of the longer side."
-Wizard of Oz, non-existent revised edition.
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The scarecrow says "the sum of the squares of two sides of an isoceles triangle is equal to the square of the other side". I only noticed this yesterday, but he should have been talking about right angled triangles, saying "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
Now PLEASE stop arguing about it!!!!
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Okay, saw it again last night. He recites utter gibberish.
He says the square roots of ANY two sides of ...
It would be correct for RIGHT triangles only if he said the sum of the square roots of the two SHORTER sides of a right triangle equals the square root of the remaining side.
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Noooooooooooooooo people! My friends and I were just watching this movie 2 seconds ago and we had seen this "slip up" prior to viewing the movie, he said that the sum of the square root of an iscoseles triangle is equal to the sum of the square root of the remaining sides..a squared plus b squared equals c squared, pythagorean theorem,...he just forgot to say that it was supposed to be a right triangle....and he forgot an s or two at the end of the words... you guys are just being picky!
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