This week’s New York Times Magazine has an article called “The Year in Ideas.” One feature in the article is “Bubble Wrap That Never Ends,” by Vanessa Gregory. She writes about the popular Japanese keychain called Mugen Puchi Puchi. It has six small buttons on it, and pressing them simulates popping bubble wrap. The keychain…
Category: Math
A new continued fraction for pi
I love continued fractions. The golden ratio: The square root of 2: The base of the natural logarithm: Pi: In the most recent American Mathematical Monthly (December 2008) Thomas J. Pickett and Ann Coleman, in their note “Another Continued Fraction for ,” present the following beautiful continued fraction in which the terms down the diagonal…
Four color theorem applets
The four color theorem is a beloved result with a long and fascinating history. The theorem says that four colors suffice to color any map so that no two bordering regions are the same color. The conjecture was made in 1852 by Francis Guthrie. After many, many failed proofs, the conjecture was finally put to…
Secrets of my success
Here are the five things I need to be a productive mathematician. 1. Time to think 2. Time to think 3. LATEX (I find most of my errors while typing my work) 4. Someone to talk to (it is great having a collaborator) 5. Coffee (I have no memory of not liking the taste of…
Euathlus and Protagoras
In my Discrete Mathematics class we discussed a few famous paradoxes, such as Russell’s paradox/barber paradox/librarian paradox, the liar’s paradox, and the naming numbers paradox. Afterward, a student of mine shared with me this old legal paradox featuring Euathlus and Protagoras. Euathlus wanted to become a lawyer but could not pay Protagoras. Protagoras agreed to…
Thoughts on how to teach induction
In their article “Some observations on teaching induction,” (MAA Focus, May/June 2008, pp. 9–10) Mary Flahive and John Lee give tips on how to teach induction. For a variety of reasons, they encourage professors to downplay proofs of theorems such as the “baby Gauss” formula for all . Indeed, I have noticed that students can…
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 ,…
Graph theory is funny
I read and laugh at Jessica Hagy’s Indexed every day. Today Jessica created the following index card titled 7 wonders of the modern world which is based on , the complete graph on 7 vertices. She has created similar index cards before, such as… : For my MBA friends (apologies to Mr. Porter) : Yes,…
What are p-adic numbers?
I am not a number theorist, but I’ve always had a distant fascination with p-adic numbers. I have a list of “neat math topics” that I want to write about on my blog, and the p-adic numbers are on that list. So I was happy to see an interesting article about them by Andrew Rich…
Jenga mathematics
I like this: on his blog The Endeavor, John D. Cook draws an analogy between strengthening a theorem and the game Jenga. Jenga is a game where you start with a tower of wooden pegs and take turns removing pegs until someone makes the tower collapse… I use the phrase “Jenga mathematics” to refer to generalizing…
David Richeson: Division by Zero 