I’m teaching the last two weeks of one of my colleagues’ Differential Equations course. I’m leading the class through a chapter on discrete dynamical systems. In preparation for the first lecture I created a couple of java applets using Geogebra. I thought others might be interested in them, so I’m linking to them here. The…
The geometry of meandering rivers
I regularly watch the Science Friday video podcast. This week they had an interesting piece on potamology (OK, I just learned that word and wanted to use it in my post: potamology is the scientific study of rivers). The podcast showcased the work Christian Braudrick and Bill Dietrich of University of California, Berkeley, who achieved…
Legendre who?
In Chapter 10 of my book, Euler’s Gem, I give Adrien-Marie Legendre‘s beautiful proof of Euler’s polyhedron formula: for any (convex) polyhedron with V vertices, E edges, and F faces, V-E+F=2. His use of spherical geometry to prove the theorem is extremely elegant. On page 88 I include the portrait of Legendre shown at right….
Math in literature
I’ve been reading some classic literature lately and was interested to see mathematics show up two of these works. Last week I read Voltaire’s Candide (1759). One of the main characters is the ridiculous Dr. Pangloss, who subscribes to Leibniz’s philosophy of optimism (or Voltaire’s take on optimism). Leibniz believed in a good and omnipotent…
Thoughts on teaching induction
I don’t plan on doing this very often, but I thought I’d re-post one of my earlier blog posts—one that I wrote a year ago, when I had many fewer readers. Now is an appropriate time for me to re-post it because I am currently teaching induction in my Discrete Mathematics course. Enjoy. In their…
Kindergarten Mathematics (part 2): a report
Last week I wrote a blog post asking for suggestions for math to present to my son’s kindergarten class. My readers posted many great comments. Thank you all. Today was the big day,… and it was a great success! I began by talking about what I do. My son introduced me as a math teacher….
Mathematical art by Kevin Van Aelst
I just stumbled upon the website of the artist Kevin Van Aelst. His photographs are scenes constructed from food and drink that take the form of mathematical and scientific images. Here are some of the mathematical pictures on his artwork page: A Cantor set made out of fried eggs Logarithmic spiral made out of crumbs…
Kindergarten mathematics
This is a call for help. My son’s kindergarten teacher has invited parents to come in and talk about their careers. I’d like to go in and talk about math. I’d like to have some interactive hands-on mathematics activities for the kids to do. I also want them to be activities outside the typical kindergarten…
Tennenbaum’s proof of the irrationality of the square root of 2
Yesterday I came a across a new (new to me, that is) proof of the irrationality of . I found it in the paper “Irrationality From The Book,” by Steven J. Miller, David Montague, which was recently posted to arXiv.org. Apparently the proof was discovered by Stanley Tennenbaum in the 1950’s but was made widely known…
David Richeson: Division by Zero 