This is the classic mis-statement of the Pythagorean Theorem by the Scarecrow after receiving his Th.D.: "Doctor of Thinkology." What he states sounds really impressive, but it's dead wrong: "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh joy, rapture, I've got a brain." Well... It's easy to provide a counterexample by using an isosceles triangle with sides of lengths 9, 9, and 4.
As an aside, have your students watch the position of the Scarecrow relative to the other characters (Dorothy, Tin Man, and Cowardly Lion). As the scenes change, the position of the Scarecrow changes! This is one of many errors found in this movie. But it doesn't make it less enjoyable, as it's an American classic.
The Simpsons Episode "$pringfield" (Tribute to The Wizard of Oz)
As Homer Simpson finds Henry Kissingers glasses in the toilet, he feels brilliant and recites word for word the Scarecrow's version of the Pythagorean Theorem (see above). The scene is included twice, once with the the regular diaglogue and once with commentary by the writers. He's corrected by the guy in the stall. For a great website on mathematics throughout the long run of The Simpsons, go to www.simpsonsmath.com.
Star Trek the Original Series Episode "Wolf in the Fold" (Calculation of Pi)
In this episode, the computer banks of the Starship Enterprise have been taken over by an alien entity. In order to drive the alien out, Spock instructs the computer to "compute to the last digit the value of pi", and then explains to Kirk why this will cause the alien to be driven out. Spock's plan is successful. This scene can be used in conjunction with the study of decimals for irrational numbers.
Want some neat information on pi? Go to www.joyofpi.com .
Cast Away (Computation of Area of a Circle)
Tom Hanks, stranded on an island after a plane crash, uses the formula for the area of a circle to find out how much of an area rescuers would have to cover in order to find him. His comparison to the size of Texas is correct. For a nice animation on justifying the formula for the area of a circle, to to www.wku.edu/~tom.richmond/Pir2.html .
Contact (Appearance of Prime Numbers in the Search for Extraterrestrial Life)
Jodie Foster plays a scientist who is searching the skies for signals of life in the universe. This scene shows her first reception of such signals in the form of a list of all the prime numbers under 100. Her explanation of the meaning of prime numbers is met by quizzical looks from her superiors, who wonder why the aliens don't just speak English. Her quote that mathematics is the only truly universal language is priceless. You can discuss the Sieve of Eratosthenes and how it is used to find primes. This site investigates the search for Mersenne Primes: www.mersenne.org .
Star Trek the Original Series Episode "Court Martial" (Exponential Expression)
Just when you thought Spock's inspiration in the scene from "Wolf in the Fold" indicates that the writers paid attention to mathematical accuracy, listen closely to Kirk's description of how the audio sensors in the spaceship will have their sensitivity magnified! This can be used when covering exponential functions, and why there is a single positive real number that is not allowed as the base of an exponential function (and of a logarithmic functions as well).
The Mirror Has Two Faces (The Twin Prime Conjecture and Teaching Technique)
There are three scenes here. The first has brilliant mathematician/lousy lecturer Jeff Bridges explaining the Twin Prime Conjecture to humanities professor/excellent teacher Barbra Streisand. The second shows her trying to help him with his teaching, while the third involves a birthday gift of cufflinks. You might want to ask students to list several pairs of twin primes past 11, 13.
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