Pentagrams and quartic polynomials

I’m still enjoying my new-found freedom that comes with the end of the semester. I’ve gotten some research done and I’ve been able to catch up on some reading. One article that I found particularly interesting was “Quartic Polynomials and the Golden Ration,” by Harland Totland, from the June 2009 issue of Mathematics Magazine. This…

The NSF totally looks like the UAW

Here’s one for those of you who are fans of the website Totally Looks Like. The last time I was in Detroit I noticed that the emblem for the National Science Foundation totally looks like the emblem for the United Auto Workers.

Computing integer sums using l’Hôpital’s rule

Now that the busy semester is over, I’ve been able to catch up on some reading. Yesterday I read William Dunham’s article “When Euler Met l’Hôpital,” in the February 2009 issue of Mathematics Magazine. The aim of the article is to showcase some of Euler’s applications of l’Hôpital’s rule in his Institutiones calculi differentialis (1755)….

Recommended readings (5/11/09)

The Calkin-Wilf tree on Wikipedia ~ I’m very excited to teach this countability argument Long-Exposure Shot of a Roomba’s Path Shows Beautifully Organized Chaos ~ Polygonal billiards in action Clay Klein bottle ~ “It’s a bad idea to put sealed items in a kiln because they will burst as they heat. It took some time…

Let’s go to the carnival

The 52nd Carnival of Mathematics is underway over at The Number Warrior. I’m glad it was resurrected. Check it out! Two other mathematical tidbits. Clue in yesterday’s NY Times crossword: Calculus pioneer. The answer: EULER. Also in today’s NY Times, the headline: U.S. Jobless Rate Hits 8.9%, but Pace of Losses Eases. When I first…

Symmetry groups of viral doilies

Are you looking for interesting examples to use in your abstract algebra course to illustrate planar objects with rotational and reflective symmetries? Tired of the usual regular polygons and corporate logos. Already shown your class ambigrams? Feeling pressured to inject biology into your mathematics courses? Look no farther. My colleague sent me a link to the website…

Maypole braid group (solutions)

Yesterday I wrote about the maypole braid group and left two questions for homework. Here are the solutions. The first question was to show that the following maypole braids could not be represented as products of . Observe that each time we apply , one strand moves clockwise and one moves counterclockwise. Thus there is…

The maypole braid group

Over the weekend I attended a May Day party thrown by one of my colleagues. During the party they had a traditional maypole dance. An example of a maypole dance is shown at left. A maypole is a tall pole with colorful ribbons attached to the top that are fanned out in a cone shape….