I have a couple links I’d not included in the recent Playful Mathematics Education Blog Carnival. Looking at them, I can’t say why.
The top page of this asks, with animated text, whether you want to see something amazing. Forgive its animated text. It does do something amazing. This paper by Javier Cilleruelo, Florian Luca, and Lewis Baxter proves that every positive whole number is the sum of at most three palindromic numbers. The web site, by Mathstodon host Christian Lawson-Perfect, demonstrates it. Enter a number and watch the palindromes appear and add up.
Next bit is an article that relates to my years-long odd interest in pasta making. Mathematicians solve age-old spaghetti mystery reports a group of researchers at MIT — the renowned “Rensselaer Polytechnic Institute of Boston” [*] — studying why dry spaghetti fractures the way it does. Like many great problems, it sounds ridiculous to study at first. Who cares why, basically, you can’t snap a dry spaghetti strand in two equal pieces by bending it at the edges? The problem has familiarity to it and seems to have little else. But then you realize this is a matter of how materials work, and how they break. And realize it’s a great question. It’s easy to understand and subtle to solve.
And then, how about quaternions? Everybody loves quaternions. Well, @SheckyR here links to an article from Thatsmath.com, The Many Modern Uses of Quaternions. It’s some modern uses anyway. The major uses for quaternions are in rotations. They’re rather good at representing rotations. And they’re really good at representing doing several rotations, along different axes, in a row.
The article finishes with (as teased in the tweet above) a report of an electric toothbrush that should keep track of positions inside the user’s head, even as the head rotates. This is intriguing. I say as a person who’s reluctantly started using an electric toothbrush. I’m one of those who brushes, manually, too hard, to the point of damaging my gums. The electric toothbrush makes that harder to do. I’m not sure how an orientation-aware electric toothbrush will improve the situation any, but I’m open-minded.
[*] I went to graduate school at Rensselaer Polytechnic Institute, the “RPI of New York”. The school would be a rival to MIT if RPI had any self-esteem. I’m guessing, as I never went to a school that had self-esteem.