and other math cartoons

I drew some cartoons for the fabulous people at Art of Problem Solving.

One of their missions is to expand and challenge eager high school students. You have an ingenious way of having online sessions through the chat window alone. (Your problem-solving sessions have reached an absurdly high proportion of first graders at MIT and U.S. Olympics team members.) More recently, they have branched out into elementary education: your Beast Academy receives rave reviews.

However, I have little to add to their curriculum efforts, but I do to do have some moaning math word games on offer that they kindly accepted. These cartoons first appeared on their social media accounts.

“Rationalization” vs. Rationalization

Rationalization of the denominator vs. "rationalization" the denominator ("it's okay the way it is, isn't it?  does anyone really care where the radical is?")

For the record, I think the rationalization of the denominator is a useful manipulation, practical to know. The same applies to the rationalization of the counter!

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

If Fermat had wider margins (he would have wandered around for a while, still refusing to provide the evidence, 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 have to see my drawing of a cat? Certainly Not.

If someone had called quaternions when they were angry, we would have them "real part," "imaginary party," the "Dummy part for stupid babies," and the "stupid stupid thing that damn it doesn't exist."

The word “imaginary” was coined as a slander, of course, and stayed around. The quaternion units j and k should consider themselves lucky not to have been exposed to the same kind of nasty nicknames!

Whenever I make a joke, I know that Randall Munroe (xkcd) or Zack Weinersmith (Saturday Morning Breakfast Cereal) probably got there first. This is the rare and embarrassing case in which they both hit me until it stopped.

Leibniz in love

Gottfried Leibniz soon regretted comparing his love affair with DX after declaring that the relationship wasn't * nothing * for him ... just less than anything.

For a variety of reasons, I think Leibniz would have been a hard guy to love.

Although path easier than Newton.

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

Shave and a haircut“And the corresponding answer”two bits“Is a 7-part musical call and response couplet, riff, or fanfare popularly used at the end of a musical performance, usually for comedic effects.

Here we go! Strange effect! Wikipedia says it’s funny, so if you think it’s a lousy play on words then you’re just ahistorical.

Rational vs. Irrational vs. We’re not 100% sure

A "rational" Number gives rational advice.  A "irrational" Number gives irrational advice.  And the number pi to pi, which appears really irrational but cannot be proven, gives a corresponding clue.

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

Even more unfortunately, it is easy to find jobs that cause knee pain.

And most unfortunate of all, it becomes difficult to avoid careers that entangle you in these bitter, all-consuming social media feuds.

For every epsilon …

Indeed, for each epsilon there is a whole family of deltas. I drew the largest such delta.

Algorithmic runtimes as explained by the selection of a restaurant



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