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I spent some time today thinking about how long it would take me to produce a table of sines and cosines by hand. Of course it depends on the density and the precision of the table, but my conclusion was that it wouldn't take excessively long. I'd start by calculating sin 1° using the Maclaurin series, then use angle addition formulas to work up to 2°, 4°, , etc, to 90°.

Not only 17³ = 4193, but also 170^{31} = 1392889173388510144614180174894677204330000000000000000000000000000000 AND 170^{33} = 40254497110927943179349807054456171205137000000000000000000000000000000000 😀

There are SO MANY examples.

189^{19} = 17896754443176031520198514559819163143441509

After the happy coincidence of n = digit-sum(nᵏ) for (n,k) = (9,2), (8,3), and (7,4), I guessed that probably there would be no more examples, and maybe, if I was lucky, one more.

I was so, so wrong.

For quite a lot of these, I think it's not at all obvious that the vertices coincide with the vertices of a regular octagon, and I might not notice it if it weren't pointed out.

Yesterday I noticed the happy coincidence:
9² = 81; 8+1 = 9
8³ = 512; 5+1+2 = 8
7⁴ = 2401; 2+4+0+1 = 7
Happy near year all!

Are there any numbers larger than 9 that are equal to the product of their base-10 digits? No. Well, maybe, if you are willing to allow sixty-twelve and six hundred sixteenty-eight …

Last night I thought of a hilariously clever topological proof that the empty set is finite, but when I went to write it up today, I realized I had been so tired I hadn't realized it was nonsense.

I mean, the theorem is ridiculous anyway, but I still feel a little disappointed.

Coloring the edges of a dodecahedron so that every face has one edge of each color turns out to be much easier than it seems at first.

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A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.

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