Magic, Drums, Squares, and Crypto
Weaving a thread through miscellaneous mathematics
The “magic” in the title of this newsletter refers to Moessner’s Magic, a remarkable theorem that in principle could have been discovered centuries ago but was discovered in 1951. All the posts featured this time are mathematical, but this one is the most accessible. Moessner’s Magic is the kind of thing you could discover by doodling, and I expect that’s what Moessner did.
Next we have a post on the sound of drums that tile the plane. More technically, it’s a post on the eigenvalues of the Laplacian on domains that can tile the plane.
The post about vibration frequencies was for any general region that will tile, and the simplest way to tile the plane is with squares. What do we get when we look at the frequencies of drums with square heads? That’s the topic of this post.
Incidentally, I tried to get Grok to generate an image of a snare drum with a square head and it absolutely refused.
The frequencies of a square membrane are proportional to a sum of squares. That raises the question of what proportion of integers are sums of squares. The answer is given by citing a theorem in this post.
(The “squares” in the title could refer to square-shaped membranes or integers like 25 or 81.)
You may have notice that I’ve been writing more about cryptocurrency lately. This is a natural extension of my work in data privacy. Crytpocurrencies are pseudonymous, but not private, though some are more private than others. They are a prime example how people can be identified without directly identifiable information.
If your company could use help with data privacy, or cryptocurrency, or both, let’s talk. We’re also available for general applied math and statistics projects.