I try to avoid doing Reading The Comics entries back-to-back since I know they can get a bit repetitive. How many ways can I say something is a student-resisting-the-word-problem joke? But if Comic Strip Master Command is going to send a half-dozen strips at least mentioning mathematical topics in a single day, how can I resist the challenge? Worse, what might they have waiting for me tomorrow? So here’s a bunch of comic strips from the 21st of April, 2015:

Mark Anderson’s **Andertoons** plays on the idea of a number being used up. I’m most tickled by this one. I have heard that the New York Yankees may be running short on uniform numbers after having so many retired. It appears they’ve only retired 17 numbers, but they do need numbers for a 40-player roster as well as managers and coaches and other participants. Also, and this delights me, two numbers are retired for two people each. (Number 8, for Yogi Berra and Bill Dickey, and Number 42, for Jackie Robinson and Mariano Rivera.)

Gene Weingarten, Dan Weingarten, and David Clark’s **Barney and Clyde** explains a person’s ability to fold a fitted sheet as following from her advanced study of topology. Topology’s a wonderful field. It’s about how shapes relate to one another, without worrying about lengths or angle measure or so. This sounds impossibly limited. But because topology requires few assumptions, its results apply widely and in surprising fields. Fascinating and difficult problems such as how proteins fold into biologically useful shapes are, mathematically, problems of topology or its related fields.

Art Sansom and Chip Sansom’s **The Born Loser** asks something I always wonder when I’m asked to rate something from one to ten. There is a reason it’s worth paying for good survey design.

Brian Boychuk and Ron Boychuk’s **Chuckle Bros** is … I’m not sure, exactly. It looks like a geometer working out through a couple of options what the shortest distance between two points might be. That reminds me of that **Far Side** showing a despairing Einstein working over the ruins of “E = mc” and “E = mc^{3}” and “E = mc^{2.1}” while the cleaning lady says everything looks *squared* away. But it does seem like too modern a setting for someone in the geometry department to be working that out, too.

One of the Gocomics commenters says it would have been funnier if the mathematician had used wavy or crooked lines for the rejected options of wavy or crooked lines. I can’t agree. I think the straight lines crossing out the wrong options is part of building the discovery. Another Gocomics commenter says that it’s only true in two dimensions that a straight line is the shortest distance between to points, and that “in three dimensions, it’s a curve”. This seems to be a confused understanding of what’s called “non-Euclidean”, or “non-rectangular” spaces.

Modern geometry noticed that space really isn’t just a bunch of room in which things can be placed. It’s that bunch of room *along with* the way you measure how far apart things are. In “Euclidean” or “rectangular” spaces we define the distance the way you remember from high school geometry. If you don’t remember that then put a ruler on your sheet of paper showing it. (It’s “rectangular” because the distance between two points is the same as the length of the diagonal of a rectangle with opposite corners at the two points.) We most often see this as two or three dimensions. But we can set up spaces that look quite like this in one, or four, or however many dimensions you like. Infinitely many dimensions, if you need that.

But not every interesting kind of space is Euclidean. For example, on the surface of the Earth the straight-line distance is useless, except for spots very close together. Any useful measure of the distance between New York City and Singapore is based on how far you go along the surface of the Earth. Well, you might go a little above, by plane, or a little below, by underwater cable, but it’s close enough to the surface. In a non-Euclidean space like the surface of a planet a straight line either doesn’t exist or isn’t interesting. The curve that does have this shortest distance is called the “geodesic”. And in a Euclidean space the geodesic is a straight line again.

Jef Mallett’s **Frazz** shows a kid having trouble with what a negative number times a negative number might be. It’s something many great minds have had trouble with. I suppose that underlying the trouble is we learn positive numbers through counting, and multiplication by groups of counting. There are four malt balls on each plate, and there are three plates, therefore, there are twelve malt balls on the table. I like this metaphor. But then we tend to learn negative numbers as debts or things missing: I owe someone four malt balls, so I have negative four malt balls. If there are three people I owe four malt balls each, I have negative twelve malt balls. And if there are three missing people each of whom I owe four malt balls then … what have I got, exactly?

Steve Breen and Mike Thompson’s **Grand Avenue** is a student-resisting-the-word-problem joke. I need a catchy name for this kind of joke.

Andertoons was really funny!

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And there’s more on the way! Sometimes I wonder if I’m his underpaid publicity agent.

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