A Bunch Of Tweets I’d Thought To Save


I’m slow about sharing them is all. It’s a simple dynamic: I want to write enough about each tweet that it’s interesting to share, and then once a little time has passed, I need to do something more impressive to be worth the wait. Eventually, nothing is ever shared. Let me try to fix that.

Just as it says: a link to Leonhard Euler’s Elements of Algebra, as rendered by Google Books. Euler you’ll remember from every field of mathematics ever. This 1770 textbook is one of the earliest that presents algebra that looks like, you know, algebra, the way we study it today. Much of that is because this book presented algebra so well that everyone wanted to imitate it.

An entry in the amusing and novel proofs. This one is John Conway’s candidate for most succinct published mathematics paper. It’s fun, at least as I understand fun to be.

This Theorem of the Day from back in November already is one about elliptic functions. Those came up several times in the Summer 2017 Mathematics A To Z. This day about the Goins-Maddox-Rusin Theorem on Heron Triangles, is dense reading even by the standards of the Theorem of the Day tweet (which fits each day’s theorem into a single slide). Still, it’s worth lounging about in the mathematics.

Elke Stangl, writing about one of those endlessly-to-me interesting subjects: phase space. This is a particular way of representing complicated physical systems. Set it up right and all sorts of physics problems become, if not easy, at least things there’s a standard set of tools for. Thermodynamics really encourages learning about such phase spaces, and about entropy, and here she writes about some of this.

So ‘e’ is an interesting number. At least, it’s a number that’s got a lot of interesting things built around it. Here, John Golden points out a neat, fun, and inefficient way to find the value of ‘e’. It’s kin to that scheme for calculating π inefficiently that I was being all curmudgeonly about a couple of Pi Days ago.

Jo Morgan comes to the rescue of everyone who tries to read old-time mathematics. There were a lot of great and surprisingly readable great minds publishing in the 19th century, but then you get partway through a paragraph and it might as well be Old High Martian with talk about diminishings and consequents and so on. So here’s some help.

As it says on the tin: a textbook on partial differential equations. If you find yourself adrift in the subject, maybe seeing how another author addresses the same subject will help, if nothing else for finding something familiar written in a different fashion.

And this is just fun: creating an ellipse as the locus of points that are never on the fold line when a circle’s folded by a particular rule.

Finally, something whose tweet origin I lost. It was from one of the surprisingly many economists I follow considering I don’t do financial mathematics. But it links to a bit of economic history: Origins of the Sicilian Mafia: The Market for Lemons. It’s 31 pages plus references. And more charts about wheat production in 19th century Sicily than I would have previously expected to see.

By the way, if you’re interested in me on Twitter, that would be @Nebusj. Thanks for stopping in, should you choose to.

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Writing About E (Not By Me)


It’s tricky to write about e. That is, it’s not a difficult thing to write about, but it’s hard to find the audience for this number. It’s quite important, mathematically, but it hasn’t got an easy-to-understand definition like pi’s “the circumference of a circle divided by its diameter”. E’s most concise definition, I guess, is “the base of the natural logarithm”, which as an explanation to someone who hasn’t done much mathematics is only marginally more enlightening than slapping him with a slice of cold pizza. And it hasn’t got the sort of renown of something like the golden ratio which makes the number sound familiar and even welcoming.

Still, the Mean Green Math blog (“Explaining the whys of mathematics”) has been running a series of essays explaining e, by looking at different definitions of the number. The most recent of this has been the twelfth in the series, and they seem to be arranged in chronological order under the category of Algebra II topics, and under the tag of “E” essays, although I can’t promise how long it’ll be before you have to flip through so many “older” page links on the category and tag pages that it’s harder to find that way. If I see a master page collecting all the Definitions Of E essays into one guide I’ll post that.