2009 Times Square New Year’s Eve Ball

We can look forward to a very mathematical New Year’s eve ball in Times Square this year. According to the Times Square website: The new Times Square New Year’s Eve Ball is a 12 foot geodesic sphere, double the size of previous Balls, and weighs 11,875 pounds. Covered in 2,668 Waterford Crystals and powered by…

Materials for a knot theory class

This is a call for help—or for suggestions, at least. I’m teaching a knot theory class next semester. I’m looking for good props to use in the class to make knots. I would like to be able to make knots such as the following (and have my students do so as well). I suppose the…

46th Carnival of Mathematics

The 46th Carnival of Mathematics is now online, hosted by Walking Randomly. I was happy to see one my blog posts listed there. Cool! These carnivals are great. I’ll have to look into how to host one in the future. I don’t know who runs them.

A 10-adic number that is a zero divisor

A few weeks ago I wrote about p-adic numbers. I mentioned that if p is not prime, then the p-adic numbers can have zero divisors; that is, there are nonzero numbers and such that . Today Foxmaths! wrote about a 10-adic number (although not using that terminology) such that (in other words is an idempotent…

The importance of definitions: chance of rain

Tomorrow’s weather forecast for Carlisle, PA, is: Windy with showers. High 58F. Winds SW at 20 to 30 mph. Chance of rain 40%. First of all, 58 degrees on December 28? Sweet! But what does “chance of rain 40%” mean? Does it mean that there is a 40% chance that it will rain at my…

How to curve an exam and assign grades

We have all given exams where the grades end up lower than we hoped. A curve is in order. How do we do it? In this post I share my thoughts on when you should (or should not) curve an exam. I give ten sample curving techniques, including pros and cons of each, I explain…

Multiple choice questions in mathematics

It must be exam time. Discussions of multiple-choice test questions are in the air. Terrence Tao has a nice post about multiple choice questions in mathematics (it is a follow-up to this post of his). He writes about the pros and cons of giving multiple choice questions in a mathematics class. For example: These quizzes give a…

Exam-time humor

A little humor for all of you who are grading or taking exams… [From failblog.org] [via Superpoop]

Fallacies, Flaws, and Flimflam it’s been good to know ya

At the end of 2008 the College Mathematics Journal will stop running its 20-year column “Fallacies, Flaws, and Flimflam.” The column was devoted to “mistakes, fallacies, howlers, anomalies, and the like”—usually found on student work. In honor of the departure of this entertaining column I submit the following FFF which was submitted as a solution…

Sharkovsky’s theorem

In this post I would like to share one of the most surprising, remarkable, and beautiful results in the study of discrete dynamical systems. It relates to an unusual ordering of the positive integers: First, some definitions. The basic object of study in a discrete dynamical system is the orbit. Let be a function from…

Facebook page for Euler’s Gem

I decided to create a Facebook page for my book, Euler’s Gem. We’ll see how it goes. I’m not convinced that people actually visit these pages more than once, but we’ll see. I’ll post reviews as they come in.

Is π the right constant?

In the November 3, 2001 issue of the Mathematical Intelligencer Bob Palais wrote an article called “ is wrong!” In it Palais does not assert that we have miscalculated the value of , just that many mathematical formulas would be more elegant if we had chosen a different value for our named constant—he thinks that…