Last Thursday I posted a bunch of links, and included:
I can't remember now why I did this, but I'm still intrigued... I went to Wolfram Alpha and typed: factor 1782^12+1841^12. It's just a bunch of big numbers. Why do I like it?On Saturday night Joshua Zucker replied:
why 1782^12+1841^12? I don't know why to factor it, but of course it equals 1922^12 (just try it on your calculator, not at Walpha of course!)Well, I wasn't thinking of the consequences, and I believed him. I was impressed that he could use his calculator to factor the huge number you'd get from 178212+184112. I didn't reach for my calculator, being comfortably ensconced in my recliner. No, I reached for Google, and I googled Josh, because I was curious about what math he might lead me to.
I found a comment he made on Cut the Knot many years ago (in 2000). So I started exploring Cut the Knot, and thoroughly enjoyed some discussions about how math uses words differently from their common usage.
Eventually I remembered my original quest and googled "1782^12+1841^12". The very first thing I got was:
Fermat's last theorem. Statement that there are no natural numbers x, y, and z such that x^n + y^n = z^n, in which n is a natural number greater than 2. ...[Fermat's last theorem was proved in 1995 by Andrew Wiles. There are lots of whole number solutions to x2 + y2 = z2, like 32 + 42 = 52. But the theorem says there are no solutions to x3 + y3 = z3, nor to equations like that with higher powers.]
Huh? But Josh said 178212+184112=192212?? Next entry I clicked on was about a Simpson's episode:
In the 1995 Halloween episode of the award-winning animated sitcom The Simpsons, two-dimensional Homer Simpson accidentally jumps into the third dimension. During his journey in this strange world, geometric solids and mathematical formulas float through the air, including an innocent-looking equation: 178212 + 184112 = 192212. Most viewers surely ignored this bit of mathematical gobbledygook.Ahh, now I get it! And I finally had a vague memory of reading a post somewhere about how 178212 + 184112 and 192212 look exactly the same if you evaluate them on a calculator. (Try it!) That must be why I had originally gone to Wolfram Alpha with this.On the fan discussion site alt.tv.simpsons, however, the equation caused a bit of a stir. “What’s going on, he seems to have disproved Fermat’s last theorem!” one fan marveled, referring to the famous claim by Pierre de Fermat—proved just months earlier—that for any exponent n bigger than 2, there are no nonzero whole numbers a, b, and c for which a^n + b^n = c^n. The Simpsons equation, if correct, would be a counterexample to the theorem, meaning that the proof had been wrong.
Meanwhile, here's the other treasures I found:
- A silly math discussion on nrich
- On simpsonsmath.com, Lisa Simpson inspires Girls Just Want to Have Sums
- I learned how to use html to do the powers right (angle brackets around sup and /sup, before and after)
Posts
I caught that when that Simpsons episode aired (you always have to be ready to rewind and pause on that show). I was the only one of my family/friends to get it.
ReplyDeleteI don't watch TV, but I can pretty much bet that I wouldn't have gotten it, one detail among so many...
ReplyDeleteYou may have seen this already, but there is a nice post at Social Mathematics about how math lingo differs from normal talk.
ReplyDeleteThanks. I hadn't seen that.
ReplyDeleteA few years ago I was part of an elaborate April Fools prank where we claimed one of my colleagues found a counterexample to Fermat's Last Theorem. We had a principal make a P.A. announcement, had a fake press release on a webpage, and everything. It was big fun. :)
ReplyDeleteDid you use this same example, or something else? Tell us more... ;^)
ReplyDeleteI don't remember! It was either the same, or something like it. Where there are so many digits in the squares, they look equivalent in a calculator.
ReplyDeleteThe joke worked because we started building it up in our classes weeks ahead of time. We all did little "oh by the way" things about Fermat, and said things like "Mr. K has been working on something really huge - but I can't talk about it yet."
I knew that was wrong immediately because the LHS has to be an odd number and the RHS has to be an even number. A power of anything ending in 1 will be odd and of anything ending in 2 will be even. So *odd* + *even* = *even* obviously could not be right. It actually comes out to
ReplyDelete2541210258614589176288669958142428526657 != 2541210259314801410819278649643651567616
I tell the story from the girl's math school at least twice a year -- when we first take the square root of both sides of an equation.
ReplyDelete(In the episode, Lisa leans in the window and shouts out in response to y^2 = 25, what does y equal? "Five!" and Millhouse corrects her)
On par with the fake Fermat-buster, there's an awful, easy expression, the nth root maybe of something involving pi or e, that evaluates to 20.0000.... but then non-zero digits a few decimal places out. I think some math folks trick computer folks to check accuracy....