Water and land, nested

Just for fun… There is a puddle… …on an island (Ryan Island)… …in a lake (Siskiwit Lake)… …on an island (Isle Royale)… …in a lake (Lake Superior)… …on a landmass (the Americas)… …surrounded by water (oceans of the world). Can you do better? (By the way, I found this neat island on my own while…

Happy tau day!

It is 6/28! Happy tau day—a day that is twice as fun a pi day! Let’s celebrate our new favorite mathematical constant:  Remember, as Bob Palais told us, is wrong! I’m a fan of tau.

12 scholarly hoaxes, randomly generated articles, and other tricky fun

Everyone loves lists. Just for fun, here’s a (very) loosely-organized list of scholarly hoaxes, randomly generated content, and other interesting tidbits. Some of these I learned about recently, some I’ve known about for a long time. Theorem of the day—This website creates randomly generated “theorems.” Rejecta Mathematica—This journal publishes only articles that have been rejected by peer-reviewed…

Movie day in topology class: the Poincaré conjecture

Today was the last day of the topology class I’ve been teaching. I decided to devote the day to the Poincaré conjecture. I started by telling the students a little about the history of the problem. Then I showed them three videos. The first video was an excellent 50-minute lecture by Fields medalist Curt McMullen…

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…

Mathematical holiday cookies at Starbucks

When I was in Starbucks the other day my eyes were drawn to the cookie display, for what did I see, but a row of cookies all decorated with ‘s! Upon closer inspection I discovered, to my disappointment, that it was not the Greek letter, but the red scarf of a polar bear. (As Homer…

Euler’s formula in a children’s book

As you may know, I wrote a book on Euler’s polyhedron formula. (Euler’s formula says that every polyhedron with V vertices, E edges, and F faces satisfies V-E+F=2.) I gave a talk recently during which I lamented that kids aren’t taught this beautiful theorem; after all, it relies only on counting, addition, and subtraction. After…

Bolzano-Weierstrass Rap

In my next real analysis lecture, we’ll be discussing the Bolzano-Weierstrass theorem. (It says that any bounded sequence of real numbers contains a convergent subsequence.) I’ll be showing my class this video in which Steve Sawin (AKA Slim Dorky) raps the complete proof of the theorem. You can read the lyrics here. He has some other…

Mathematical spellcheck fail

I love my Macs, so it pains me to post this. All three of my Macs think that “Pythagoras” is a misspelling. That fact doesn’t bother me—there are a lot of proper nouns missing from the spellcheck dictionary. What hurts is that the spellchecker suggests Pythagorus as a correction. See screenshot below. C’mon Apple! You’re…