Dr. Nestler's Math 2 Precalculus
We consider the scene from the 1939 film The Wizard Of Oz in which the Scarecrow receives his brain, and the introductory scene from the episode $pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling) of The Simpsons in which Homer finds a pair of eyeglasses in a public restroom. Homer's recitation is the same as the Scarecrow's, although Homer receives a response:
Homer: The sum of the square roots of any two sides
of an isosceles triangle is equal to the square root of the remaining side.
Man in bathroom stall: That's a right triangle, you idiot!
1. What are Homer and the Scarecrow attempting to recite? Identify the error or errors in their version of this well-known result. Is their statement true for any triangles at all? If so, which ones?
2. Is the correction from the man in the stall sufficient? Give a complete, correct statement of what Homer and the Scarecrow are trying to recite. Do this first using only English words, and a second time using mathematical notation. Use complete sentences.
3. Think of another mathematical formula that you know well. As before, give a complete statement of the mathematical result that is encapsulated by the formula. Write it first using only English words, and then again using mathematical notation.
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