One of the most prolific and interesting math bloggers and Twitters, John D. Cook (his blog is The Endeavor and he is @JohnDCook on Twitter) has been using Twitter in a very interesting way. In addition to his personal account, he has set up more than half a dozen daily Twitter messages on a variety of…
Mathematical cousins and collaboration numbers
A couple days ago Michael Lugo at God Plays Dice shared a link to a mathematical relationships search. Enter the names of two people with PhDs in mathematics and it will spit out their academic relationship. For example, my advisor, John Franks, is my academic father and my good friend and collaborator Jim Wiseman is my academic…
An Euler line geogebra applet
Lately I’ve been thinking a lot about Euler and his many contributions to mathematics. So, just for fun I decided to make a Geogeba applet showing the “Euler Line.” In 1763 Euler proved that three different centers of a triangle—the centroid, the orthocenter, and the circumcenter—are collinear. This line is called the Euler line. The centroid…
Everyday geometry: hat size
I don’t wear hats very often. Occasionally I wear a baseball hat. Twice a year I wear the hat that accompanies my academic regalia. If you need to buy a hat, the first thing you need to know is your hat size. If you Google “hat size” then you can find many charts that match…
Woo hoo! A power of 10! Hooray! Here’s to an arbitrary milestone!
(A power of 10 that is, not a power of 10 factorial.) According to the WordPress.com stats, my blog has now had been viewed 100,000 times (and no, they tell me that they are not including my own visits to divisbyzero.com). Actually, as you can see below, it has been visited 100,006 times. It was…
Making a hyperboloid out of skewers and rubber bands
George Hart, of the Museum of Mathematics, writes a weekly column at Make Magazine called “Math Monday.” A few weeks ago he showed how to make a hyperboloid of one sheet out of 32 shish kabob skewers and 176 hair rubber bands. (Here is a direct link to the instructions.) We just finished talking about…
Perelman to be awarded the Clay Millennium Prize
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:…
A card trick that will probably amaze your friends (solution)
Warning! Spoiler alert! This post contains the secret behind the card trick that I described in my last post. Read that post before reading this one. First the bad news: this card trick is not fool-proof; it is a probabilistic card trick. The good news is that in my experience, it has a high probability…
A card trick that will probably amaze your friends
Here’s a neat card trick that I learned a few years ago. I can’t remember where I read about it. If anyone knows the source of trick, please post it in the comments. [Update: I now know more about the origin of this trick. I’ll write more in my follow-up post.] Thoroughly shuffle an ordinary…
An application of graph theory to architecture
Several years ago I came across a fascinating application of graph theory to architecture. It is in the 1983 book Incidence and symmetry in design and architecture, by Jenny A. Baglivo and Jack E. Graver. I don’t know if it is well known among experts in the field, but I’ve never seen it elsewhere. So…
David Richeson: Division by Zero 