Pinned toot


It's late. I misread a notification as “favourited your cactus”.

I was momentarily excited to discover that János Pach has a blog! But then I saw that it has only one nontrivial post, from 2010.

In which I complain about mathematical jargon and identify some candidates for the worst example.

…Professor Snorfus, the world's foremost expert in the theory of smooth prime numbers…

The set of real and pure imaginary numbers is analogous to the set of even and odd functions $\Bbb R→ \Bbb R$.

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!

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