Dan Drake 🦆I'm absurdly excited to learn that 2024 = 2³+3³+4³+5³+6³+7³+8³+9³.
...and it's because:
2025 = 45², and
45=1+2+⋯+9, and
(1+⋯+𝑛)²=1³+⋯+𝑛³ !
Via https://www.reddit.com/r/math/comments/18tr14a/2024_2³3³4³5³6³7³8³9³/.
Blobster@ddrake Nice, thanks!
BTW, do you know of a convenient way on Linux (maybe using LaTeX-style markup) to enter equations as in your message, with the Unicode math characters (the special 𝑛 aka U+1D45B MATHEMATICAL ITALIC SMALL N, integer powers, etc.)?
P.S.: Those who wonder why (1+⋯+𝑛)²=1³+⋯+𝑛³ can sum the relations
(𝑘(𝑘+1)/2)² − (𝑘(𝑘−1)/2)² = 𝑘³
for 𝑘 from 1 to 𝑛.
@blobster I don't know if this is specific to my instance -- Mathstodon -- but when I use the regular web app to enter stuff, it has an option for converting LaTeX markup to Unicode -- see the screenshot.
@ddrake Thanks for your reply! Indeed, I believe this feature is specific to your instance.
@blobster it is, but we're not selfish. 🙂 You can contact @christianp for details; @mwt has it working for their amusingly-named econtwitter mastodon instance...
shower thought: with The Site That Was Twitter now being called X, I like the idea that "twitter" could be a generic term for this kind of social media site, revolving around short-ish posts/tweets that are usually visible to everyone.
(This matches interestingly with Cory Doctorow's ideas of breaking up social media companies, of interoperability, and also matches the language he uses in his recent book The Lost Cause, where he uses "the twitters" to refer to just this kind of idea.)