Christian Lawson-Perfect @christianp@mathstodon.xyz

On matters of notation: sometimes your convenience is my confusion.

Pretty sure my gender is not computable in polynomial time. You could say I'm NB-complete.

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 [1]:

n! ≈ nⁿ · e⁻ⁿ · √(2πn)

[1] https://en.wikipedia.org/wiki/Stirling's_approximation

#maths

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.

Elliptic functions really look lovely in domain coloring plots. I made this one to have a triple pole and a triple zero.

Finally joined this thing, so here is an old image I did of the Boy surface

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.

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.

Kernel Density Estimation
https://mathisonian.github.io/kde/

Une chouette animation pour comprendre ce que KDE signifie
#visualization #statistic #math
https://shaarli.buron.coffee/?aR8-PQ

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... !!
https://en.wikipedia.org/wiki/Fibonacci_word

Does anyone want to see one of my favorite memes

Our kid has this super cute planter and I looooooove it