Linkage

Infinite Sudoku and the Sudoku game. The game is to alternate choosing values (with no repetitions allowed per row, column, or smaller square) until stuck. Joel Hamkins provides a complete analysis of who wins, not only on any finite \(n^2\times n^2\) board, but also in an analogous infinite game where one player is trying to fill the entire board and the other is trying to block a solution.

Coloring problems for arrangements of circles (and pseudocircles). In connection with Aubrey de Gray’s breakthrough on the Hadwiger–Nelson problem, Gil Kalai posts some related problems on coloring circles.

Convert LaTeX markup to unicode text). Likely useful for underfeatured social media like Google+ that don’t allow MathJax.

Three-gap theorem. New Wikipedia article on the mathematics behind the spacing of plant leaves and the intervals of musical scales.

Girl-guide dreamcatchers tile the plane with similar kites. One of them looks like the kite-only version of my diamond-kite meshes, or would if the girls were more accurate.

Anna Haensch collects links on the origins of mathematical notation (via). See also Bret Victor on THE BIG INTEGRAL.

Sašo Krajnc, aka Cvern, creates portraits from intricate string art. It’s just a circular frame and a loop of string that visits every peg around the frame once. How could it produce any kind of complicated picture? But it does.

How poetry and math intersect. As Evelyn Lamb writes, “Both require economy and precision—and each perspective can enhance the other.”

Area-proportional Venn diagrams (via). The goal is not only to have a desired pattern of intersections, but to have the areas of each intersection approximate some desired target. It’s straightforward for two circles via binary search, but for larger numbers (where there might not be an exact solution), which heuristics are most accurate?

The Justice Department deleted language about press freedom And racial gerrymandering from its internal manual (via). It may not come as much of a surprise that the current US administration is not among those of us interested in fixing the problems of gerrymandered and politically and racially biased electoral districts…

Gauss’s braid: braided paper strips as a method for form generation. “Gauss’s braid” more commonly refers to a specific element of the four-strand braid group, used by Gauss as an example in his work on an integral formula for the linking number. Gauss was interested in this because of the possibility that planetary orbits might be linked; see “Orbits of asteroids, a braid, and the first link invariant” (Epple 1998) for details. Gauss’s braid is shown in Epple’s Figure 2, which credits it as “Page 283 of Gauss’s Handbuch 7”. While searching for all this, I found this link on paperforms. I don’t see how it has much to do with Gauss (whose birthday is today), but it still looks interesting.