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…

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)….

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…

Happy Valentine’s Day

For your reading pleasure: The Calculus of Saying “I Love You”: Why you should never date man who knows more math than you.  (I wouldn’t say the mathematics is perfect, but it is fun to read.) Also, from xkcd.com:

Why do mirrors reverse right and left but not up and down?

Stand in front of a mirror and hold up your right hand. The person standing in the mirror holds up her left hand. Why is that? Why does a mirror reverse left and right? After all, it does not reverse up and down. Before we answer that question, we have to ask a more basic…

Calculus and sustainability

I saw a number of interesting talks while at the Joint Mathematics Meeting last week. Hopefully I’ll find the time to write about some of them here. One of the presentations that got me the most excited was the minicourse that I attended, Educating about the state of the planet and sustainability while enhancing calculus,…

Definition of continuity video

Thank you to Dansmath for turning me on the website xtranormal. It allows you to create your own animated videos. It is easy and fun. You can choose the characters, the scene, the camera angles, the gestures and facial expression, music, etc. They do the voices for you—you just type the script. Here are some of Dan’s videos….

The prime number theorem in Calculus II

I attended Shahriar Shahriari’s MAA Minicourse Beyond Formulas and Algorithms: Teaching a Conceptual/thematics Single Variable Calculus Course at the 2008 Joint Mathematics Meeting. He talked about having his calculus students derive the prime number theorem. Recall that the prime number theorem states that if is the number of primes less than or equal to ,…

The sum of kth powers

Everyone loves the “baby Gauss story” in which Gauss amazes his teacher by quickly summing the first 100 positive integers in a flash of brilliance—he adds the first to the 100th, the second to the 99th, and so on to get the sum of fifty 101s to obtain 5050. (Brian Hayes has a great article…

Calculus in politics

In his October 1996 editorial in the Notices of the American Mathematical Society, “Mathematics Is an Edifice, Not a Toolbox,” Hugo Rossi wrote: In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his…