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Close only counts in horseshoes. And applied maths by Adam Hrankowski, maths/physics tutor in BC.
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| A Fermat near miss looks like a bull’s eye — until you examine it up close. |
You may know Fermat’s Last Theorem, that 350-year-old conundrum to which Andrew Wiles published a solution in 1995. Seventeenth-century lawyer/mathematician, Pierre de Fermat remarked in the margin near Problem II.8 of Diophantus’s Arithmetica (I hope it wasn’t a library book!) that there were no positive integer solutions for the equation,
when n > 2, and a, b and c are all non-zero. He added that he had a “truly marvelous demonstration of this proposition that this margin is too narrow to contain” — an understatement, indeed, since Wiles’s solution spans over 100 pages, and relies on mathematics developed since the time of Fermat.
A 1995 episode of The Simpsons presented viewers with a counterexample:
You can verify the following with a calculator:
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| Screen shots of the author’s calculator illustrate the Fermat Fandangle. |
What sort of wizardry is this?
Something is afoot. On the left-hand side, we have an even number. (Any power of an even number, such as 1782 will be an even number.) This, we add to an odd number. (Any power of an odd number, such as 1841 will be an odd number). Adding an even number to an odd number gives us an odd number. Always. But the right-hand side is even. So, unless something has gone awry with basic number theory, Wiles’s reputation is safe.
Depending on the calculator you used, you may have spotted the trickery after the eighth decimal place, where the right and left-hand sides depart from each other. We have here a Fermat near miss — almost, but not quite, so not at all. And here is where we distinguish pure maths from applied maths...
With applied maths, the mathematics models the physical universe. (Or does the physical universe model the mathematics? That’s another discussion.) Therefore, I advise mathematics students to avoid the π key on their calculators, which can only approximate an irrational solution.
Recommended Reading
When Am I Ever Gonna Use This Stuff?:
A Playful Romp Through the Artform Disparagingly Known as Precalculus
This is the maths textbook your mother warned you about... by Adam Hrankowski.
Source: Medium
