If Fermat Had Wider Margins

and other math cartoons

I’ve been drawing some cartoons for the fabulous folks at Art of Problem Solving.

One of their missions is to extend and challenge eager high schoolers. They’ve got an ingenious way of running online sessions through chat window alone. (Their problem-solving sessions have reached some absurdly high fraction of MIT first-years and US Olympiad team members.) More recently, they’ve branched into primary education: their Beast Academy gets rave reviews.

Anyway, I have little to contribute to their curricular efforts, but I do have some groan-worthy math puns on offer, which they graciously accepted. These cartoons first appeared on their social media accounts.

“Rationalizing” vs. Rationalizing

Rationalizing the denominator vs. "Rationalizing" the denominator ("it's okay like it is, right? does anyone really care where the radical is?")

For the record, I view rationalizing the denominator as a useful manipulation, handy to know. Same goes for rationalizing the numerator!

But I view the tradition of compelling students always to rationalize the denominator as a bit silly. Sure, it’s nice to have a “standard form” for radicals (which can otherwise be written so many different ways). But the main justification for rationalizing the denominator (that it’s easier to divide 1.4121 by 2 than to divide 1 by 1.4121) no longer holds in an age of ubiquitous calculators.

If Fermat Had Wider Margins (he would have rambled for a while, still refusing to provide the proof, and instead filled the missing space with a picture of a cat)

Did the world need another Fermat joke? Maybe not.

But did the world need to see my drawing of a cat? Definitely not.

If someone had named quaternions when they were angry, we'd have the "real part," "imaginary party," the "make-believe part for silly babies," and the "stupid dumb part that doesn't friggin' exist."

The word “imaginary,” of course, was coined as a slur, and it stuck around. The quaternion units j and k should feel lucky they were not subject to the same kind of nasty nicknaming!

Whenever I make a joke, I’m aware that Randall Munroe (xkcd) or Zack Weinersmith (Saturday Morning Breakfast Cereal) has probably gotten there first. This is the rare and embarrassing case where they both beat me to the punch.

Leibniz in Love

Gottfried Leibniz soon regretted comparing his romantic relationship to dx, after explaining that the relationship was not *nothing* to him... just less than any possible something.

For a variety of reasons, I think Leibniz would have been a tough dude to love.

Although way easier than Newton.

For those of you unfamiliar with early 20th-century vaudeville references, Wikipedia explains:

Shave and a Haircut” and the associated response “two bits” is a 7-note musical call-and-response coupletriff or fanfare popularly used at the end of a musical performance, usually for comedic effect.

There you go! Comedic effect! See, Wikipedia says it’s funny, so if you think it’s a lousy pun, then you’re just being ahistorical.

Rational vs. Irrational vs. We’re Not 100% Sure

A "rational" number gives rational advice. An "irrational" number gives irrational advice. And the number pi to the pi, which really seems irrational but cannot be proven so, gives advice to match.

Unfortunately, it’s hard to find stable, rewarding careers.

Even more unfortunately, it’s easy to find careers that cause knee pain.

And most unfortunately of all, it’s getting hard to avoid careers that embroil you in those bitter, all-consuming social media feuds.

For Every Epsilon…

Really, for every epsilon, there exists a whole family of deltas. I have drawn the largest such delta.

Algorithmic Runtimes as Explained Through Choosing a Restaurant

6 thoughts on “If Fermat Had Wider Margins

    1. For those that had never heard of it before, the most famous example of the “shave and a haircut two bits” motif is Not Fade Away by the Rolling Stines.

  1. When you get to calculus and beyond, you are free to write 1/√2 or √(1/2). Until that time you must show that you understand the algebraic manipulations.

    1. Definitely agree that knowledge of the algebraic manipulations is important. I’m fine with students demonstrating that knowledge in other ways. But then again, I’m also fine with a teacher requiring them to demonstrate knowledge by always rationalizing denominators.

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