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In the original book by author and Oz series originator Lyman Frank Baum [May 15, 1856-May 5, 1919], the Wizard removed the Scarecrow's head, for adding bran, needles, and pins to top out the straw. The Scarecrow felt that the Wizard had given him a brain, because Dorothy Gale noticed how the top bulged out. The Tin Woodman noticed the needles and pins sticking out of his friend's head. The Wizard explained that they showed the Scarecrow's sharp wit. In the 1939 film version, the Wizard gave a paper by which the Scarecrow had an honorary Th.D., or Doctorate in Thinkology. The Scarecrow immediately put his finger to his head, and made the impressive-sounding observation of the sum of the square roots of any two sides of an isosceles triangle equaling the square roots of the remaining side. Hardly! For example, a triangle that's 36 x 49 x 64 has the square roots of 6, 7, and 8. Adding 6 to 7 doesn't make 8, but 13. Adding 7 to 8 doesn't make 6, but 15. And adding 8 to 6 doesn't make 7, but 14. Instead, the true statement is the square of the hypotenuse of a right triangle equaling the sum of the squares of the other two sides. For example, a triangle that's 3 x 4 x 5 has the squares of 9, 16, and 25. The hypotenuse is the longest side. And adding 9 to 16 makes 25.

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15y ago
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12y ago

The Scarecrow was able to say "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."

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Jagger Jacobson

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2y ago

The crow

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Q: How did the Scarecrow figure out that the Wizard had given him a brain?
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