Dr. Nestler's Math 2 Precalculus

Homer/Scarecrow worksheet

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!”
        Homer:  “D'oh!”

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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