We can think of a mathematical knot as a knotted piece of string (or in our case, wire) with its free ends joined. Examples are shown below. There is a remarkable theorem that every knot can be realized as the boundary of a surface. Moreover, Herbert Seifert produced a very simple algorithm for constructing an orientable…
Congress designates 3/14 National Pi Day
In the news: Ya can’t make it up: House praises pi National Pi Day? Congress makes it official Here’s the vote on C-Span. The vote was 391 yeas, 10 nays, 30 not voting. Who were the 10 Representatives who voted against it? Jason Chaffetz (R-Utah) Jeff Flake (R-Arizona) Dean Heller (R-Montana) Timothy Johnson (R-Illinois) Jeff…
The area versus the circumference of a circle
I just found this stop motion animation that I made last year when I was playing around with the iStopMotion software. So I uploaded it to YouTube and posted it here for you all to see. It is not the highest quality, but it was fun to make. It shows the Greek method of relating…
Putting mathematical scholarship in perspective
At our college tenure decisions (as well as other personnel and salary decisions) are made by an all-college committee with faculty members from a variety of departments. There must be at least one faculty member from the sciences, but there may be no mathematician on the committee. Thus it is extremely important for the chair…
Recommended readings (3/12/09)
An ancient typo ~ Has no one noticed this before?!? Stackable letters ~ A new way to classify letters of the alphabet Mathematician answers Supreme Court plea ~ A fair division problem for voting Wolfram|Alpha is coming! ~ The next Segway or the next Google? An Appel a day ~ Seven colors suffice for a…
Flashlights and conic sections
Recently, Ξ over at the 360 blog wrote about hyperbolic light (which was inspired by the article, “The Shape of Lamp Shade Shadows” by Kenneth E. Horst, The Physics Teacher, Volume 39, March 2001). They were looking at the pattern of light on the wall emitted by a desk lamp with a cylindrical lampshade. They observed that the…
Sines and cosines (part 2)
In my previous post I asked the following question. What -values satisfy the equation ? More generally, let and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? First, let us look at some properties of the iterates of and . is periodic with…
Sines and cosines (part 1)
A friend asked me the following question. What -values satisfy the equation ? It occurred to me to ask a more general question. Let and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? Is it possible answer this question? Always? Sometimes? Never? I’ll post my…
New graduation requirement
One of my colleagues sent me the link to the most recent comic at xkcd.com. He wrote: “College graduates should be required to say why this is funny as a condition of graduation, a part of numerosity.”
Top 8 most popular polygons
Web surfers love lists—best Twitter apps, best albums, greatest films, world’s richest, best colleges (no, wait, we’re not supposed to like this list). So, I thought I’d serve up a list for my audience. The top 8 most popular polygons. My inspiration The idea for this list came to me while my kids were watching…
David Richeson: Division by Zero 