The Week in Meep: Sumo and Geometry Book Recommendations

Some brain-ticklers

First, let’s get the sumo out of the way…

That was a week ago, and today is nakabi, aka halfway-day. The yokozuna has currently got a solid lead, and slippery, hot Nagoya is doing its thing, with rikishi falling left and right with injuries.

I’ve got two favorite matches right now — Terunofuji v. Ura, where Ura threw everything he had at the top guy… and Ryuden v. Midorifuji, which had something of a surprise ending.

I’m not going to embed those fights, as the videos tend to be yanked fairly rapidly by NHK, so in lieu of that, enjoy a couple of frogs fighting:

Separately, on my sumo stats substack, I generally don’t post much during the tournament, but here’s my post on Terunofuji’s stats:

Profile Line-Up Before Nagoya - Plus Terunofuji

Okay, and here’s a fun picture:

via @ten10kozo

More Math Book Recommendations

On Father’s Day, I mentioned some math books I really liked:

And a little bit ago I got into recommending these and more on twitter.

So let me offer a few more math-y recommendations, of a variety of levels.

For this week, my theme will be geometry.

Interested in visualizing higher dimensions? Or what geometry is?

How about:

• Flatland by Edwin Abbott Abbott: Gutenberg project link

• Sphereland by Dionys Berger: Amazon link to Sphereland/Flatland dual edition

• Flatterland by Ian Stewart: Amazon link

• The Fourth Dimension by Rudy Rucker: Amazon link to a Dover Illustrated edition from 2014 (I have an older edition)

One of the biggest issues I’ve had with school math is that they generally destroy all the wonder from it by making it be something that has to be about proofs and calculations, and not something that can be about mental exploration just for the hell of it.

The above books (not Flatterland - that was published when I was an adult) were all ones I read as a kid, and helped me enjoy geometry so much more. I hated geometry as a subject in school, except for constructions (“Construct a regular pentagon with this side using only a compass and a straightedge”)

So why not blow your mind with higher-dimensional geometry?

Note: NONE OF THESE HAVE FORMULAS OR PROOFS OR HOMEWORK.

(Or if they ever did, I forgot it — I read all of these for fun.)

Flatland by EAA is the granddaddy of them all, published in 1884. It’s partial social critique but mainly trying to explain higher spatial geometry by having a sphere visiting Flatland (an infinite plane) to talk to a square living in Flatland. Via analogy to 2-d experiencing 3-d visitor, one thinks through how 4-d might work intersecting 3-d space.

The square and sphere visit 1-d Lineland at one … point in the plot

Sphereland extends the idea further, by including ideas of curved space from non-Euclidean geometry and general relativity. In this one, a hexagon, grandson of the square from the original book, meets a surveyor who has measured a triangle with angles adding up to more than 180 degrees.

Rudy Rucker’s Fourth Dimension is a very accessible book about how to think about four spatial dimensions. It is packed with illustrations and notes. Here are a couple of examples of the concept of degrees of freedom - we may be in 3-dimensional space, but can move only with 2 or 1 degrees of freedom, depending.

Finally, the oddest of the four books, Ian Stewart’s Flatterland isn’t really about higher dimensions, but what, exactly, is geometry anyway? This gets into very non-Euclidean geometry - I don’t like Ian Stewart as much as my usual go-to popular math authors, but he treats subjects the others don’t. I still think it’s worthwhile, even if I don’t think the execution is that great.

This is too weird! I want normal geometry!

I can do that, too!

Oliver Byrne’s Elements of Euclid - the millennia-old classic is brought to life in full color, courtesy a Victorian mathematician.

The website - a bit pretentious as it has both the “long s” (that looks like a f) and a short s (the normal kind).

But it is pretty.

I have the paperback edition I bought via Amazon, eminently readable, and very beautiful.

It tickles my brain.