Before Watching
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Let students explore the equation xn +
yn = zn by substituting
different values for n. Have them begin with n =
2, resulting in the familiar Pythagorean Theorem, x2 + y2 = z2.
Then have students change the value of n to numbers
greater than 2 to see whether they can find solutions that will
result in a balanced equation with a positive integer answer for
z.
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To be sure that xn + yn =
zn has no solutions when n is a
positive integer greater than 2, every value for n needs
to be checked—a nearly impossible feat, even with the aid
of a computer. A proof is needed. Review with students the
concept of theorem, a mathematical statement that can be proved,
or awaits proving. Then ask them to describe ways that things
can be proved in non-mathematical contexts, such as in law,
mystery novels, or in their everyday lives. How do these types
of proofs compare to mathematical proofs?
After Watching
-
Ask students to list the traits Anderw Wiles needed to solve
Fermat's Last Theorem. Which traits seem most important? Which
seem least important?
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