Hallo, new Mastodon users! Here on mathstodon.xyz we've got a couple of mathematical emoji: and . I'd love to add some more. If you can make a PNG image the same size as those, send it to me and I'll add it. Faces of famous mathematicians are an easy place to start; could we have some shapes, polyhedra, or other mathographics too?
A friend told me that
n! ≤ nⁿ
was the only thing he could say about how fast factorials grow. Well, he's not that far, because we have Stirling's formula :
n! ≈ nⁿ · e⁻ⁿ · √(2πn)
Regular polygon surfaces: https://arxiv.org/abs/1804.05452
Ian Alevy answers Problem 72 of The Open Problems Project (http://cs.smith.edu/~jorourke/TOPP/P72.html#Problem.72): every topological sphere made of regular pentagons can be constructed by gluing regular dodecahedra together.
You can also glue dodecahedra to get higher-genus surfaces, as in this image from https://momath.org/mathmonday/the-paragons-system/, but Alevy's theorem doesn't apply, so we don't know whether all higher-genus regular-pentagon surfaces are formed that way.
Why software projects take longer than you think – a statistical model at https://erikbern.com/2019/04/15/why-software-projects-take-longer-than-you-think-a-statistical-model.html - discuss at https://freepo.st/freepost.cgi/post/f2a8xbu4mu #freepost
@christianp @JordiGH To me, this sort of goes back to the question of whether functions are valued which depend on other values (a la early mathematicians and most physicists) or machines which take and spit out values (computer scientists and most modern mathematicians). A lot of modern notation and terminology is an uneasy mix of the two, and I’d love to see some better way of reconciling them which preserves the benefits of both.
#MastoAdmin I just cleared 11G of preview cards from my instance. Why isnt' there a tootctl command for this? Are they supposed to be cleaned up automatically?
off on a tangent: did you know that the clear stuff (vitrious humor? aqueous? we forget which) in your eyeballs can scintillate when struck by charged particles, and make your eyes act like little cosmic ray detectors?
retinas are sensitive - it only takes about four photons to activate a rod cell in near-total darkness - and astronauts have talked about seeing blue flashes with their eyes closed all the time while in space, especially in higher orbits.
I've just updated mathstodon.xyz to Mastodon v2.8.0.
Release notes: https://github.com/tootsuite/mastodon/releases/tag/v2.8.0
It's got polls, an interface to manage your follow lists, and lets us change signups from open access to "ask for an invitation". We'll do that if spam becomes a problem again (it currently isn't)
Came across the fibonacci word the other day: s₀=0 s₁=01 sᵢ =sᵢ₋₁||sᵢ₋₂ (string concatenation). The limit is 0100101001001... seems to have only a passing resemblance to the fib numbers... but look at y=x/φ in R² and consider where it intersects the grid with vertices in N² - write a 0 when it intersects a vertical line and 1 when it intersects a horizontal line and you get 0100101001001... !!
Mathematician, koala fan, mathstodon.xyz admin,
⅓ of https://aperiodical.com
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
\) for inline LaTeX, and
\] for display mode.