How to morph graphs on the torus, with Erin Chambers, Patrick Lin, and Salman Parsa: http://jeffe.cs.illinois.edu/pubs/morph.html
Found in Friedman's _A History of Folding in Mathematics_, p. 71, a quote from Francesco Maurolico from 1537: "Item manifestum est in unoquoque regularium solidorum, numerum basium coniunctum cum numero cacuminum conflare numerum, qui binario excedit numerum laterum".
Except for the fact that he considers only Platonic solids, this is Euler's formula V-E+F=2 for convex polyhedra (in the equivalent form V+F=E+2), long before Euler (1752) and Descartes (1630).
A quasi-polynomial algorithm for well-spaced hyperbolic TSP: https://arxiv.org/abs/2002.05414
This new preprint by Sándor Kisfaludi-Bak (accepted to SoCG) just came out and caught my attention. TSP is NP-hard for Euclidean points or close-together hyperbolic points. This paper shows that it's much easier when the points are widely spaced in the hyperbolic plane. The idea is to separate the input by a short line segment that the solution crosses few times and apply dynamic programming.
One of the first non-trivial straight skeletons (as a roof model), from _Kotirte Ebenen (Kotirte Projektionen) und deren Anwendung_ by Gustav A. von Peschka (1877). See https://en.wikipedia.org/wiki/Straight_skeleton
Consider the algorithm "M(x): if x<0 return -x, else return M(x-M(x-1))/2". This algorithm terminates for all real x, though this is not so easy to prove. In fact, Peano Arithmetic cannot prove the statement "M(x) terminates for all natural x". Paper to come! Joint work with @jeffgerickson and @alreadydone
In which we show that the knots K13n592 and K15n41127 (pictured) both have stick number 10. These are the first non-torus knots with more than 9 crossings for which the exact stick number is known.
Article by Erickson, Jeff
In collections: Unusual arithmetic, Easily explained
Update on the Safe ToC initiative: https://windowsontheory.org/2019/08/30/update-on-the-safe-toc-initiative-guest-post-by-sandy-irani/
Sandy Irani describes progress in combatting harassment and discrimination at theoretical computer science conferences, and calls for volunteer advocates to serve as contact points at conferences.
$400 online calculus course for full (transferrable) credit at Pitt: https://outlier.org/calculus
While it's tempting to call this a MOOC, but it's not open. Let's give them the benefit of the doubt and call it a MOC.
(Written when the author was 11, and submitted when he was 12. See the affiliation "Jr. High School 246" on the last page of the article, and the letter from the author's mother on page 91 of the same issue.)
https://aeon.co/essays/how-european-sailors-learned-celestial-navigation — "Soon after this, mariners started cramming for exams. Instead of paying 36 florins for an entire winter of lessons, Amsterdam-based mariners paid just 6 florins for a crash course focused on the oral and written portions of the tests. Later manuscript workbooks confirm this strategy: students often focused on the questions they knew would be on their exam. Teachers at the close of the 17th century were already ‘teaching to the test’."
CS professor at Illinois
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