That's the set of all integers that are (a) \( 2^i3^j \), (b) \( 5k\pm1\), and (c) at least \(54\).

Consider the family F that contains the subsets of \(\Bbb Q\) that are closed under multiplication. Some elements of F are well-known (\( \varnothing\), \( \Bbb Q \) itself; others less so. (Consider the set of rational numbers with denominators of the form \( 5k \pm 1\)] or the set with denominators \( 2^i3^j\) .)

\( F \setminus\{\varnothing\} \) has a very interesting lattice structure.

Dividing a chocolate bar into any proportions: https://mathoverflow.net/questions/338888/dividing-a-chocolate-bar-into-any-proportions

The bar has L squares, and you want to give each of m people an integer number of squares, but the integers are not known in advance. How to break the bar into few pieces so this will always be possible?

Reid Hardison asked this months ago but Ilya Bogdanov answered with an efficient construction of the optimal partition much more recently.

Quasiperiodic bobbin lace patterns: https://arxiv.org/abs/1910.07935, Veronika Irvine, Therese Biedl, and Craig S. Kaplan, via https://twitter.com/bit_player/status/1185356703065354240 — aperiodic tilings in fiber arts.

The attached image is a photo of lace (not an illustration), braided into an Ammann–Beenker tiling pattern.

New math post on my blog: More fair cake-cutting https://blog.plover.com/math/cake-2.html

New math post on my blog: Incenters of chocolate-iced cakes https://blog.plover.com/math/cake.html

New math post on my blog: Breaking pills https://blog.plover.com/math/breaking-pills.html

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- Totemic animal spirit
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I am an amateur mathematician, but not the angle-trisecting kind.

Joined May 2017