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Pythagorean Theorem ala the Wizard of Oz Scarecrow

Probably all of you have seen the original version of The Wizard of Oz. It is a classic....but not as classic as the statement made by the Scarecrow when he is given some brains and awarded his Th.D, or Doctorate in Thinkology.

First, visit the TeacherTube site for a view of this part of the movie. Click on the video of the mathematical scarecrow.The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

Some things to investigate with students:

  • Is this phrase recited in the original book version?
  • Is the scarecrow's statement ever true?
  • What would the geometrical world look like if the statement was always true?
  • Have you seen The Simpsons's episode where Homer retrieves Henry Kissinger's glasses from a toilet, puts on the glasses, and promptly recites the Scarecrow's mangled phrase...prompting a man in an adjacent toilet stall to call out "That's a right triangle, you idiot!"
  • Dr. Nestler's worksheet on the quote
  • The inclusion of the Pythagorean Theorem in other movies
If you want to further investigate the mathematics underlying the scarecrow's claim, check out these resources:
  • Leake, L. (1986). “Did the scarecrow really get a brain? An analysis of the Scarecrow's Pythagoras-like statement in The Wizard of Oz.” Mathematics Teacher, Vol. 79, pp. 438 - 439
  • Pancari, J. and Pace, J. (1987). “Two Views of Oz: Using the Scarecrow's Pythagorean-like utterance to define the fundamental isosceles triangle of Oz.” Mathematics Teacher, Vol. 80, pp. 100 - 101
  • Mathbits worksheet
  • The Scarecrow Conjecture Activity, a student paper