Experiments on reverse perspective: paulbourke.net/miscellaneous/r

Recent post by Paul Bourke with a link to a recent video, youtube.com/watch?v=iJ4yL6kaV1, "Hypercentric optics" by Ben Krasnow, showing how to achieve reverse perspective physically using a giant Fresnel lens

US Department of Homeland Security decides to require foreign students in the US to either attend in-person classes or leave the country: ice.gov/news/releases/sevp-mod, via news.ycombinator.com/item?id=2

Or to put it another way, they are pressuring US universities into opening up in-person classes despite the ongoing pandemic, using the threat of taking away all of their foreign students.

A tiny improvement sometimes makes for a big result: In a new preprint "A (Slightly) Improved Approximation Algorithm for Metric TSP" (arxiv.org/abs/2007.01409), Anna Karlin, Nathan Klein, and Shayan Oveis Gharan claim a reduction in the approximation ratio for traveling salesperson in arbitrary metric spaces from \(\tfrac{3}{2}\) to \(\tfrac{3}{2}-10^{-36}\). But it's the first such improvement since Christofides and Serdyukov in 1976, on a central problem in approximation algorithms.

0xDE boosted

Matthew Seymour has done more incredible work in service of the connection game Hex, this time in the form of a beautifully-implemented collection of 500 "white/black to play and win" puzzles of the sort that chess and go enthusiasts take for granted as study tools:

mseymour.ca/hex_puzzle/hexpuzz

arXiv-worthy is almost the same as journal-worthy. When I'm not convinced it's worth the effort to do all that but I want it out there in some form, I tend to write a blog post, but that has the disadvantage of not being properly in the scientific literature for people to cite when they need something formal to cite (like as a reference in a Wikipedia article).

What is it about Quanta's oversimplifications? A recent article quantamagazine.org/new-geometr is on a variation of the problem of squares in Jordan curves (en.wikipedia.org/wiki/Inscribe), known to exist in smooth curves but unknown for some nastier ones. The new result finds rectangles of given aspect ratio in smooth Jordan curves (arxiv.org/abs/2005.09193). Wikipedia editors have had to fend off repeated edits by Quanta readers who came away thinking the new paper solved the original problem. It doesn't.

A stained glass window of a Latin square (en.wikipedia.org/wiki/Sir_Rona) will be removed from Cambridge U. (theguardian.com/education/2020) because it honors prominent eugenicist R. A. Fisher (en.wikipedia.org/wiki/Ronald_F).

The window visualizes a nice piece of mathematics, with a long history that surprisingly originates in Korea (predating Euler) but in context among windows celebrating Cambridge luminaries it could not be separated from Fisher's racist history, so it's sad but I think it's the right decision.

A power struggle between the Georgia state university system and state government blocks Georgia Tech and other campuses from enacting any coronavirus safety rules: chronicle.com/article/georgia-

This year's London Math Soc. prizewinners: lms.ac.uk/news-entry/26062020-

Via Holly Krieger at twitter.com/hollykrieger/statu, who won one of this years Whitehead Prizes.

For some reason they keep the Louis Bachelier Prize separate from this listing; it's at lms.ac.uk/prizes/louisbachelie

These results have already led me to add to Wikipedia brief articles on Maria Bruna (another Whitehead Prize, en.wikipedia.org/wiki/Maria_Br) and Pauline Barrieu (Bachelier 2018, en.wikipedia.org/wiki/Pauline_).

@christianp @ColinTheMathmo My suspicion is that like in community.netlify.com/t/enabli the local mathstodon.xyz content security policy is blocking the mathstodon.xyz mathjax script

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@christianp @ColinTheMathmo Javascript console is showing lots of error messages "Refused to apply inline style because it violates the following Content Security Policy directive: "style src='self' mathstodon.xyz". Either the 'unsafe-inline' keyword, a hash ('...') or a nonce ('nonce-...') is required to enable inline execution.

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New blog post: Sorting with integer offsets 11011110.github.io/blog/2020/0

For inputs \( x_i \) and a parameter \( k \), sorting the set \( \{x_i+j \mid 0\le i\lt n, 0\le j\lt k\} \) more quickly than a pure comparison sort is a nice exercise in radix sorting. But sorting the very similar-looking set \( \{jx_i \mid 0\le i\lt n, 0\le j\lt k\} \) seems much harder. Why? And what does this all have to do with greedy set cover?

@christianp @ColinTheMathmo MathJax on Mathstodon is broken for me on Chrome (both logged in and not). All formulas are plain text and ugly. But if I switch to Firefox the formatting is still ok. MathJax on other sites is also still ok. Any suggestions (besides ditching Chrome)?

Today I learned, while writing a Wikipedia article on Doyle spirals (en.wikipedia.org/wiki/Doyle_sp) that although the pure-mathematics work in this area dates to Coxeter in 1968 and the work of Thurston and his followers in the 1980s and 1990s, the use of spiral patterns of tangent circles to model plant growth can be traced back much earlier, to Gerrit van Iterson in 1907. The image below, which I used as the lead for the article, comes from a 1911 Popular Science story about plant growth.

QCSP monsters and the demise of the Chen conjecture: dl.acm.org/doi/10.1145/3357713

In STOC'20, Zhuk and Martin show that dichotomy for constraint satisfaction (see en.wikipedia.org/wiki/Schaefer) gets messier for quantified CSP. Chen conjectured that QCSP problems are either in NP or PSPACE-complete, but coNP-completeness can happen for 3 elements and more elements lead to even more classes.

Talk video: youtube.com/watch?v=c2HjFlcTjQ

Zhuk just won the Presburger Award: eatcs.org/index.php/component/

Does anyone know what's up with the Mathematics Genealogy Project? I haven't been getting any response from its servers for a week or so.

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