These are the last of the comics from the final full week of June. Ordinarily I’d have run this on Tuesday or Thursday of last week. But I also had my monthly readership-report post and that bit about a particle physics simulator also to post. It better fit a posting schedule of something every two or three days to move this to Sunday. This is what I tell myself is the rationale for not writing things up faster.

Ernie Bushmiller’s **Nancy Classics** for the 27th uses arithmetic as an economical way to demonstrate intelligence. At least, the ability to do arithmetic is used as proof of intelligence. Which shouldn’t surprise. The conventional appreciation for Ernie Bushmiller is of his skill at efficiently communicating the ideas needed for a joke. That said, it’s a bit surprising Sluggo asks the dog “six times six divided by two”; if it were just showing any ability at arithmetic “one plus one” or “two plus two” would do. But “six times six divided by two” has the advantage of being a bit complicated. That is, it’s reasonable Sluggo wouldn’t know it right away, and would see it as something only the brainiest would. But it’s not so complicated that Sluggo wouldn’t plausibly know the question.

**Eric the Circle** for the 28th, this one by AusAGirl, uses “Non-Euclidean” as a way to express weirdness in shape. My first impulse was to say that this wouldn’t really be a non-Euclidean circle. A non-Euclidean geometry has space that’s different from what we’re approximating with sheets of paper or with boxes put in a room. There are some that are familiar, or roughly familiar, such as the geometry of the surface of a planet. But you can draw circles on the surface of a globe. They don’t look like this mooshy T-circle. They look like … circles. Their weirdness comes in other ways, like how the circumference is not π times the diameter.

On reflection, I’m being too harsh. What makes a space non-Euclidean is … well, many things. One that’s easy to understand is to imagine that the space uses some novel definition for the distance between points. Distance is a great idea. It turns out to be useful, in geometry and in analysis, to use a flexible idea of of what distance is. We can define the distance between things in ways that look just like the Euclidean idea of distance. Or we can define it in other, weirder ways. We can, whatever the distance, define a “circle” as the set of points that are all exactly some distance from a chosen center point. And the appearance of those “circles” can differ.

There are literally infinitely many possible distance functions. But there is a family of them which we use all the time. And the “circles” in those look like … well, at the most extreme, they look like squares. Others will look like rounded squares, or like slightly diamond-shaped circles. I don’t know of any distance function that’s useful that would give us a circle like this picture of Eric. But there surely is one that exists and that’s enough for the joke to be certified factually correct. And that is what’s truly important in a comic strip.

Sandra Bell-Lundy’s **Between Friends** for the 29th is the Venn Diagram joke for the week. Formally, you have to read this diagram charitably for it to parse. If we take the “what” that Maeve says, or doesn’t say, to be particular sentences, then the intersection has to be empty. You can’t both say and not-say a sentence. But it seems to me that any conversation of importance has the things which we choose to say and the things which we choose not to say. And it is so difficult to get the blend of things said and things unsaid correct. And I realize that the last time **Between Friends** came up here I was similarly defending the comic’s Venn Diagram use. I’m a sympathetic reader, at least to most comic strips.

And that was the conclusion of comic strips through the 29th of June which mentioned mathematics enough for me to write much about. There were a couple other comics that brought up something or other, though. Wulff and Morgenthaler’s **WuMo** for the 27th of June has a Rubik’s Cube joke. The traditional Rubik’s Cube has three rows, columns, and layers of cubes. But there’s no reason there can’t be more rows and columns and layers. Back in the 80s there were enough four-by-four-by-four cubes sold that I even had one. Wikipedia tells me the officially licensed cubes have gotten only up to five-by-five-by-five. But that there was a 17-by-17-by-17 cube sold, with prototypes for 22-by-22-by-22 and 33-by-33-by-33 cubes. This seems to me like a great many stickers to peel off and reattach.

And two comic strips did ballistic trajectory calculation jokes. These are great introductory problems for mathematical physics. They’re questions about things people can observe and so have a physical intuition for, and yet involve mathematics that’s not too subtle or baffling. John Rose’s **Barney Google and Snuffy Smith** mentioned the topic the 28th of June. Doug Savage’s **Savage Chickens** used it the 28th also, because sometimes comic strips just line up like that.

This and other Reading the Comics posts should be at this link. This includes, I hope, the strips of this past week, that is, the start of July, which should be published Tuesday. Thanks for reading at all.