RE: https://mastodon.social/@thejapantimes/116582909254485186 This is highly irregular. Kissei must have been really spooked about the observed adverse effects of avacopan to basically defy their marketing partner, Amgen. Likely at great cost to themselves, but this could also turn out like the […]

RE: https://mathstodon.xyz/@tpfto/104252234949024822 I still feel the same way to this very day. Especially after reading a paper where all the variables I was interested in happen to be of the opposite sign convention used in the paper. Having to flip signs while programming was a chore.

自分のできることなら、LLMなんていらないぞ！

Something I did not mention in the previous posts on Salas et al.'s paper on trigonometric approximations to elliptic functions was that to plot the Costa and Chen-Gackstatter minimal surfaces, I also needed to derive a compatible approximation to the Jacobi epsilon function […]

In a series of previous toots, I talked about a paper by Salas, Martinez, and Ocampo (https://doi.org/10.1155/2021/5546666) about trigonometric approximations to elliptic functions, especially the Jacobi elliptic functions. The paper also mentions the Weierstrass functions, but I've found their […]

I generally find that the people who are fond of "move fast and break things" often tacitly exclude themselves from the list of "things that might get broken in the process". Hence the callous disregard often observed.

Once again, I ask for the kindness of strangers: please help me get copies of https://doi.org/10.1007/s00190-026-02034-z and https://doi.org/10.1007/s10543-025-01055-y . #icanhazpdf

Consider the time 7:30. It seems most languages use some variation of "half" when talking about this time, but differ in whether the half is "before" or "after". In English, one can say "half past seven". In Spanish, you say "son las siete y media" (literally, "seven and half"). (Filipino […]

I recently found this paper by Salas, Martinez, and Ocampo (https://doi.org/10.1155/2021/5546666) that features simple trigonometric approximations to the Jacobian elliptic functions. To test them out, I decided to use them to plot Costa's minimal surface ( […] [Original post on mathstodon.xyz]

I mentioned an article on how kids of this age barely have a concept of a "file" or a "directory" (https://archive.is/pCD0N) in a response to one of @AmenZwa's posts a little while ago, which suddenly made me remember something from back when I was still in uni. I was in the Internet café […]

I'm trying to find a paper I read so many months ago on asymptotically evaluating \\(\prod_{k=0}^\infty(1-a q^k)\\) as \\(q\to1^{-}\\), but I've even forgotten who the authors were. I've already seen the excellent paper of Banerjee and Wilkerson (https://doi.org/10.1142/S1793042117501135) on […]

This may very well be too late to write about, but: does the "inurl:" keyword not really work anymore on Google? I keep getting the same crummy pap in my search results despite multiple attempts to fiddle with keywords. This makes the "use the FABULOUS search engine" admonition of old times even […]

In my neck of the woods, they seem to have recently released a coin with a QR code in it: https://www.bsp.gov.ph/SitePages/CoinsAndNotes/ASEAN-Coin.aspx . Never thought I'd see the day... #philippines

The thread on surprising facts you found out recently by @johncarlosbaez was getting a bit long, so I'm posting this entry separately: if I'm understanding https://en.wikipedia.org/wiki/Mohorovi%C4%8Di%C4%87_discontinuity#Exploration correctly, no manmade device has yet reached the Moho, the […]

I recently updated an old shader of mine on Shadertoy (https://www.shadertoy.com/view/3tf3WS) demonstrating approximations to the CIE color matching functions (https://en.wikipedia.org/wiki/CIE_1931_color_space#CIE_XYZ_color_space), which attempt to model the tristimulus nature of human color […]

I just ran into some annoying behavior in GLSL, or at least the version on Shadertoy. As it turns out, in the built-in mod operator m % n, if m is negative, the result of the operation becomes 0. I was wondering for the better part of the day why stuff that came out smooth in Mathematica […]

The Hantangang (https://english.visitkorea.or.kr/svc/contents/contentsView.do?vcontsId=33717) is a popular whitewater rafting destination in South Korea. It also happens to be the place that gave its name to the hantaviruses, which were first discovered in rodents isolated from that area. I'm […]

Now, more than ever, I find myself contemplating the last two sentences from this page of Acton's "Numerical Methods that (usually) Work".

I recently made this GLSL shader: https://www.shadertoy.com/view/N3fGzr to show off a method due to Miroslav Fiedler (https://en.wikipedia.org/wiki/Miroslav_Fiedler) for getting a triangle's circumcircle and incircle.

For a few hours, I fiddled around a little bit with @peterluschny's "Swiss knife polynomials" (http://www.luschny.de/math/seq/SwissKnifePolynomials.html) \\(\mathcal{W}_n(x)\\), and I thought I'd record a few things here. These all derived from the fact that they have the EGF \\(\exp(x […]

Arithmetic is perhaps a little lowbrow for Mathstodon, but this clip of virtual YouTuber Tokino Sora drilling fellow virtual YouTuber Sakura Miko in arithmetic with signed numbers might prove pedagogical for some: https://youtu.be/6lCqiIVla3E

I just noticed that the wiki article on Dixon elliptic functions (https://en.wikipedia.org/wiki/Dixon_elliptic_functions) is still pointing to two Math Stack Exchange threads I answered a long time ago.

Currently making considerable headway on documenting stuff related to elliptic functions. At some point, when I have access to a proper computer that can run git, I really ought to be making the Python functions I wrote public. (I personally do not find […] [Original post on mathstodon.xyz]

Once again, I need to rely on the kindness of strangers. Please help me get these two papers: https://doi.org/10.1017/S0004972723000424 and https://doi.org/10.1007/s40627-025-00168-y. #icanhazpdf

My backlog of "stuff I really should be writing up for the arXiv" is slowly yet steadily growing. Unfortunately, 1. they need to be organized and massaged into something other people will actually read; and 2. I'm not connected to any academic institution, so I don't have anyone who can endorse […]

People who are used to the Western system of counting with large numbers often have trouble when they first learn the Japanese or Chinese systems. This mostly boils down to differences in how we partition powers of 10. In the Western system, after the sequence of "tens, hundreds, thousands", all […]

RE: https://mathstodon.xyz/@tpfto/116442731607734242 Thanks to an e-mail exchange with Cormac O'Sullivan, who wrote a lovely paper on "De Moivre polynomials" (https://arxiv.org/abs/2203.02868), the polynomials that are otherwise called "partial ordinary Bell polynomials" in the literature, I […]

I'm currently looking at the elliptic functions that were studied by Patrick Du Val (https://doi.org/10.4064/aa-9-2-133-147) and further investigated by Robinson (https://doi.org/10.1017/S0004972725100713). I find that Du Val's elliptic functions, by virtue of […] [Original post on mathstodon.xyz]

Searching for mathematical identities on the Internet is often difficult, moreso if the identity has not ever been named after someone. For instance, I recently found an expression for the generalized Nørlund-Bernoulli polynomial (denoted as NorlundB[n, a, x] in Mathematica) in terms of the […]

Took a bit of time, but here's a domain coloring visualization of the Dixon elliptic functions in Shadertoy: https://www.shadertoy.com/view/7fBSDD To me, the threefold symmetries of sm(z) and cm(z) give the visualization a kaleidoscopic feel. #math #mathart

Quite a while back, the Borwein brothers studied the so-called "cubic theta functions" while investigating cubic analogues of the arithmetic-geometric mean iteration (https://doi.org/10.1090/S0002-9947-1994-1243610-6). These three functions […] [Original post on mathstodon.xyz]

Since @johncarlosbaez posted about tetrahelices (https://en.wikipedia.org/wiki/Boerdijk%E2%80%93Coxeter_helix) the other day, I thought I'd share something I recently made on Shadertoy: https://www.shadertoy.com/view/sfBXDR . If you look at the implementation closely, I generate the points of […]

Two people I do not particularly care for are getting married, and had just sent me an RSVP the other day. I responded thus, "Apologies, I will not be able to make it on that day due to prior commitments. Nevertheless, may the two of you keep on deserving each other."

I'm now five-for-five on e-mailing people about acquiring a copy of the code described in their papers, and them apologizing since they no longer have the relevant files for a paper many years old. This effectively renders their papers difficult to replicate, unless I try coding their methods […]

I hadn't had access to a device with Internet access until very recently, so I am trying to catch up on some of the manga series I had been reading. Last week's installment of "Tune In to the Midnight Heart" somehow spoke to me, as someone putting stuff out on the Internet.

Having a spot of trouble finding a free and fully online Python environment that would let me install rdkit and mpmath.

Some time back, I did a write-up about a theorem on triangles often attributed to Napoleon Bonaparte, and its generalization to affine regular polygons by Barlotti: https://community.wolfram.com/groups/-/m/t/3416619

Sometimes the world feels flat to me…

I don't think I'm in the right headspace to start making math art again just yet. (Nor do I have a nice computer to do stuff in, for that matter.) For now, here's a cute application of linear interpolation I wrote a few years ago: https://www.shadertoy.com/view/wlsGWN

It's already been decades since I first learned about this word problem, but the solution still makes me giggle: > A mother is 21 years older than her daughter. Six years from now, the mother will be 5 times as old as the daughter. Where's the father?

As the use of LLMs keeps becoming more and more pervasive on the Internet, my (some say) stubbornness on not even using autocomplete to help me write stuff does seem a bit quaint these days. The only time I really use autocomplete is when I write in Japanese. The technology does seem to be […]

There's a paper I am looking at that claims to present an explicit formula for the Padé approximant of a certain special function. However, cursory experiments indicate that the rational functions coming out of that purported formula are quite different from the Padé approximant you get from the […]

I suppose this could be considered a soft return to posting online of sorts. I don't exactly have reliable access to any sort of computing device just yet, and I am kind of starting to miss being able to write code on an actual computer. Let's see how stuff develops…

I was able to borrow a smartphone for today. Just for fun, I decided to write an implementation of the partial (exponential) Bell polynomial (https://en.wikipedia.org/wiki/Bell_polynomials#Exponential_Bell_polynomials) in Python: https://pastebin.com/bZnpVTP1 . SymPy has it, but not NumPy or […]

I thought it was time for a makeover, so I decided to pick one of my experiments with Bohemian matrices for my avatar. Here's a slightly larger version:

Still on a Bohemian matrix kick, here's a visualization of the eigenvalues of Bohemian matrices with upper arrowhead structure, with entries picked from the fifth roots of -1.