Hidden amid its trademark satire of common American life, The Simpsons is riddled with mathematical Easter eggs. The present’s writing employees has boasted a formidable pedigree of Ivy League mathheads who couldn’t resist infusing America’s longest-running sitcom with inside jokes, scattered about like sprinkles on Homer’s doughnuts.
As early because the opening shot of the present’s second episode, the perpetually one-year previous child, Maggie, stacks her alphabet blocks to learn EMCSQU. Little doubt an homage to Einstein’s well-known equation E = mc2.
There’s an episode the place Homer tries to turn into an inventor and he engineers a number of harebrained concepts, together with a shotgun that blasts make-up in your face and a recliner with a built-in rest room. Throughout a brainstorming frenzy, Homer scribbles some equations on a chalkboard together with:
198712 + 436512 = 447212
This references Fermat’s Final Theorem, one of the crucial notorious equations in math historical past. The potted model, should you haven’t come throughout it: seventeenth century mathematician Pierre de Fermat wrote that the equation an + bn = cn has no entire quantity options when n is bigger than 2. In different phrases, you possibly can’t discover three entire numbers (non-decimal numbers like 1, 2, 3…) a, b, and c such that a3 + b3 = c3 or a4 + b4 = c4, and so forth. Fermat wrote that he had “found a really marvelous proof of this” however couldn’t match it within the margin of his textual content. Later mathematicians discovered this message and, regardless of the easy look of the declare, did not show it. It went unproven for over 4 centuries till Andrew Wiles lastly cracked it in 1994. Wiles’ proof depends on strategies much more superior than what was obtainable in Fermat’s day, which leaves open the tantalizing chance that Fermat knew of a extra elementary proof that now we have but to find (or his supposed proof had a bug).
Plug Homer’s equation into your calculator. It checks out! Did The Simpsons discover a counterexample to Fermat’s Final Theorem? It seems that Homer’s trio of numbers represent a near-miss. Most calculators don’t show sufficient precision to detect the slight discrepancy between the 2 sides of the equation. Author David X. Cohen wrote his personal laptop program to seek for near-miss options to Fermat’s infamous equation all for this split-second gag.
This week’s puzzle comes from the season 26 finale, wherein the denizens of Springfield take part in a mathlete competitors. The episode is full of mathematical goodies, together with the little joke beneath posted exterior of the competitors. Are you able to decipher it?
The climactic tie-breaking geometry drawback is more durable than it seems. I hope it doesn’t make you shout, “D’oh!”
Did you miss final week’s puzzle? Test it out here, and discover its answer on the backside of in the present day’s article. Watch out to not learn too far forward should you haven’t solved final week’s but!
Puzzle #20: The Simpsons M
Add three straight traces to the diagram to create 9 non-overlapping triangles.
The triangles might share sides, however shouldn’t share inside house. For instance, the left-hand determine beneath depicts two triangles, whereas the right-hand determine solely counts as one triangle, as a result of the bigger triangle overlaps with the smaller one.
I’ll publish the reply subsequent Monday together with a brand new puzzle. Are you aware a cool puzzle that you simply assume ought to be featured right here? Message me on Twitter @JackPMurtagh or e-mail me at firstname.lastname@example.org
Answer to Puzzle #19: Psychological Illusions
How did you fare on final week’s problems? I in contrast them to optical illusions as a result of each puzzles seem at first blush to require some concerned calculation. However when you understand the hidden trick, the answer snaps into focus like Necker cubes abruptly inverting. Each puzzles are literally gimmes, with the appropriate perspective. Shout-out to reader McKay, who submitted two appropriate solutions over e-mail.
1. It’s going to take at most one minute for the entire ants to fall off an finish of the meter stick. It appears difficult to trace the oscillating habits of every ant. Couldn’t they bobble backwards and forwards without end? If you squint your eyes, you’ll see that the situation the place two colliding ants instantly swap their instructions isn’t any totally different from the case the place the ants transfer proper by way of one another! In each instances, there will likely be ants at precisely the identical factors alongside the stick strolling in the identical path.
Think about every ant was carrying a bit prime hat and every time two collide they immediately swap hats earlier than carrying on in the wrong way. Observe a single prime hat’s path and also you’ll discover that it simply beelines for one finish of the stick at a continuing tempo the entire time. Since ants transfer at one meter per minute and the longest any ant might should journey is the complete size of the meter stick, the entire ants will attain an finish of the stick inside one minute.
2. How concerning the geometry drawback?
What’s the size of AC?
It seems SAT-ready. Possibly the Pythagorean theorem is so as. Maybe a trigonometric identification or two. Blink twice and the phantasm of complexity vanishes. The road connecting factors O and B can also be a diagonal of the rectangle and can have the identical size as AC. Solely OB is extra helpful as a result of it’s a radius of the circle! The diagram tells us the circle’s radius alongside the x-axis: 6+5 = 11, our reply.