Just overheard an argument that reinforces my contention that world peace is impossible for as long as people can't agree on whether pineapples belong in pizza.

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.

Clearly, there's a lot of things to try out; I might come back to this subject every so often. (Both pictures were generated thanks to the function featured in mathematica.stackexchange.com/ .)

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This one, on the other hand, came from 5ร—5 upper Hessenberg matrices with the same rules for the superdiagonal entries, but with a zero diagonal and a subdiagonal of -1.

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Since @rcorless was posting about Bohemian matrices a while ago, I thought I'd try some experiments of my own. Here's the result of plotting the eigenvalues of 4ร—4 upper Hessenberg matrices with zero diagonal and the other entries chosen among the cube roots of -1.

Featured below, for instance, is a plot of the book's parametric equations for buccoli. I'd been thinking about new stuff to do for math art, and this seems to drum up some fresh ideas.

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Recently, a kind friend gave me a copy of the lovely book "Pasta by Design" (thamesandhudson.com/pasta-by-d), which features proposed parametric equations for common and not-so-common pasta shapes. Plotting these in Mathematica gave nice results, as expected, but looking at the forms of the equations, I can't help but feel that some of those can certainly be tweaked...

This page by Robert Ferrรฉol (mathcurve.com/surfaces.gb/gour) features Goursat surfaces that have icosahedral symmetry. I've always wondered if it's possible to get a surface that looks like a rounded version of the truncated icosahedron, but I have not been successful in tweaking the formula from that page.

For better or for worse, I've been really busy for the past few months. Hopefully, I'll have some more time again to do some cute math art. Here's something I did 10(!) years ago, in the meantime:

@JordiGH just checking, have you already noticed that you are following 666 accounts?

I don't remember anymore if I had shared this WebGL thing I made showing a Newton-Raphson fractal on the Riemann sphere here: shadertoy.com/view/wtXGDB

Since @esoterica recently tooted an article about envelopes, here's one of my favorites, showing that the nephroid can be considered as either an envelope of lines or an envelope of circles:

I hate that the phrase "doing your own research" is getting ruined for autodidacts like me.

I just got the molecular modeling kit I ordered in the mail. To test it out, I made a buckyball:

The Japanese animated series "Science Fell in Love, So I Tried to Prove it" (or "Rikekoi" for short), which is a romcom about two researchers, recently announced a second season: twitter.com/rikeigakoini/statu . What is perhaps most interesting for the purposes of this Mastodon instance is that their logo for this season incorporates the plot and the polar equation of the cardioid (en.wikipedia.org/wiki/Cardioid), \(r=1-\sin\theta\).

I got my second shot of the Pfizer vaccine today (despite multiple factors that seemed bent on preventing me from getting to the hospital). I'm sure I'll be knocked flat for the next few days, so I tried to do what I can with this project I'm doing involving weird peptides.

The recent @esoterica posting reminded me of this little gem on elliptic functions, for some reason: doi.org/10.1119/1.1285882 . (Note that this is a different Erdรถs altogether!)

Overheard: "A triangle where the side lengths are not Pythagorean? That can't be right!"

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