Mathematically, I can't say much. I did some work with (nonsmooth) dynamical systems as an undergrad, and now I'm interested in many things such as Nathan Kutz's work on data-driven modeling of dynamical systems (e.g. SINDy, koopman linearization).
Academically, I recently got back in school for an MS (and hopefully PhD eventually). I'm trying to get through my classwork and qualifying exams in order to start doing research again.
Thanks for having me!
Light reflecting off Christmas-tree balls
Web page by Joseph O'Rourke
In collection: Easily explained
'Twas the night before Christmas and under the tree Was a heap of new balls, stacked tight as can be. The balls so gleaming, they reflect all light rays, Which bounce in the stack every which way. When, what to my wondering mind does occur: A question of interest; I hope you concur! From each point outside, I wondered if light Could...
My paper where I prove the optimality of the smallest known sorting networks with 11 and 12 channels is out on arXiv: https://arxiv.org/abs/2012.04400
Those were known since 1969, but whether smaller exist was an open problem since. 1/n
156. THE DISSECTED TRIANGLE. A good puzzle is that which the gentleman in the illustration is showing to his friends. He has simply cut out of paper an equilateral triangle--that is, a triangle with all its three sides of the same length. He proposes that it shall be cut into five pieces in such a way that they will fit together and form either two or three smaller equilateral triangles, using all the material in each case. Can you discover how the cuts should be made?
Wikipedia: all the right facts, not necessarily in the right order.
You could think of this game as "the Collatz sequence with a running total" - what happens next doesn't just depend on which number you're on now, it also depends on all the numbers you've seen before.
Think of a number, and keep a running total starting at 0. Each turn, add your number on to the total. Then, if the old total was a multiple of your number, add one to your number. Otherwise, subtract 1.
The game ends when your number is 1.
Which starting numbers eventually get to 1? In the video, it looks like starting at 4 doesn't, but starting at 2 does.
My new sequence, https://oeis.org/A338807, lists the numbers that eventually reach 1. I'd love to know if there's a pattern!
I've got a new sequence in the OEIS. It's to do with a really simple number game I made up. Here's a video explaining the rules
@christianp I'm not sure of the precise meaning, but one cannot fail to notice that it is an anagram of "Oil Suit Technocrat," which is probably a significant clue.
4. THE BEANFEAST PUZZLE. A number of men went out together on a bean-feast. There were four parties invited--namely, 25 cobblers, 20 tailors, 18 hatters, and 12 glovers. They spent altogether £6, 13s. It was found that five cobblers spent as much as four tailors; that twelve tailors spent as much as nine hatters; and that six hatters spent as much as eight glovers. The puzzle is to find out how much each of the four parties spent.
Here's an amusing if minor repeated typo in the literature: "appiled superconductivity", https://scholar.google.com/scholar?q=%22Appiled+Superconductivity%22 (177 hits). I think the source is IEEE, which spells Trans. on Applied Superconductivity correctly on its site but misspells it repeatedly in the doi database. So if you get your citations from doi metadata, you will get this error.
You can see the metadata for a doi by doing curl -LH "Accept: application/x-bibtex" on the url for the doi. Try e.g. 10.1109/TASC.2005.849553
Corker of a line from https://www.stephendiehl.com/posts/exotic01.html
“And the story of computation has been about the evolution of this very novel and peculiar form of human expression we call code. I suspect being a programmer in the 21st century must be like what being a royal scribe was like in Ancient Egypt in 3200 BCE. There’s this new modality of communication that most of the population is unaware of, yet it’s existence simultaneously enables commerce, culture and civilization to flourish.”
Mathematician, koala fan, mathstodon.xyz admin,
⅓ of https://aperiodical.com. He/him
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