The epilogue of my book is devoted to the Poincaré conjecture, the famously challenging 98-year old topological puzzler that was proved in 2002 by Grisha Perelman. Perelman was awarded the Fields Medal in 2006 for this accomplishment, but he declined to accept the award. Today the Clay Mathematics Institute issued a press release that begins:…

# Tag: topology

## A tale of why you (U, that is) needs a tail

What is this collection of symbols? No, it is not a wallpaper border pattern, a brain teaser, or ancient hieroglyphics. It is a set identity, of course! When I was in college I had a math major friend who said that all he learned in our topology class was to put tails on his U’s…

## What is the cardinality of the Euclidean topology?

I’m teaching topology this semester. The students are looking at different topologies on the real number line. For homework I asked them to think about which topologies are “the same” (if any) and which are “different,” and why they thought that was the case. We haven’t yet talked about continuous maps or homeomorphisms, so I…

## A new way to collaborate: DropBox

I have a long-time collaborator who lives in Georgia (I’m in Pennsylvania). I’ve had good luck collaborating with him via email, but it is a pain. As soon as one of us edits a file he sends it to the other person as an email attachment. We haven’t had any “forked” files, but we do…

## 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….

## How to use KnotPlot

As I’ve mentioned before, I’m teaching a knot theory class this semester. I’ve been playing around with KnotPlot, a powerful piece of software for drawing and working with knots. I want my students use it, but it has a somewhat unintuitive interface. So I’m trying to write up a list of easy-to-use instructions for them. The…

## 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…

## Möbius bubble wrap

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…

## 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…

## Lipson’s mathematical LEGO sculptures

Ξ at the the 360 blog just posted a neat LEGO fact: it is possible to snap together two 2×4 lego bricks in 24 different ways. Given six of these LEGOs it is possible to snap them together in 915,103,765 different ways! This inspired me to post a link to a cool website by Andrew Lipson….