Take a collection of real-world data such as the lengths of all rivers in the world, the populations of counties in the United States, the net worths of American corporations, or the street addresses of all residents of Detroit. Strip away all the information except the leading digits. What percentage of these digits do you…
Category: Math
A game for budding knot theorists
Thanks to Sam Shah for introducing me to this fascinating online game: Entanglement. The rules are simple. You are given hexagonal tiles, one at a time, each adorned with six short segments of rope. Use them to construct the longest possible knot (measured in segments) before running into a wall. Entanglement is fun and addicting!…
Mathematical surprises
I’m interested in compiling a list of “mathematical surprises.” The best possible example would be a mathematical discovery that no mathematician saw coming, but after it was discovered it changed mathematics in some fundamental way—Cantor’s discovery of the nondenumerability of the continuum is such an example. But I’ll settle for any surprise—Andrew Wiles surprised everyone…
Goodstein’s unprovable theorem
Recently I learned about a family of sequences of nonnegative integers (called Goodstein sequences) and two remarkable theorems about these sequences. Begin with any positive integer . This is the first term in the sequence. For example, suppose we begin with . The first step in computing the second term of the sequence, , is…
The left-handed boy problem
A few months ago Gary Foshee was scheduled to speak at the Gathering for Gardner. He got up and gave a presentation that was all of three sentences. He said: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? This deceptively simple problem quickly made…
Mathematical magic tricks for kids
My six-year-old son loves the website ActivityTV.com, especially their science, origami, cooking, and magic videos. I watched a few of the magic how-to videos with him and was pleasantly surprised to see that some of them had a distinctly mathematical feel to them. For example: Jumping rubber bands: topological properties of circles and linked circles…
Thirteen mathematically-inspired products
Just for fun, here is a list of 13 mathematically-inspired products that I’ve stumble upon recently. Klein bottle house Come in/Go away ambigram doormat Klein bottle bottle opener Chair made of Voronoi cells Tiling a floor with irregular pentagons A Möbius bridge The Pittsburg Steelers logo (and my blog post about it) Nesting Fibonacci kitchen…
Tricks for easily creating BibTeX files
I wrote my last book (my only book, that is) using LaTeX. I had a large bibliography with close to 400 entries. I stored all of the bibliographic items in a BibTeX file (a text file ending in .bib). Each item looks something like this: @book {Richeson:2008, AUTHOR = {Richeson, David S.}, TITLE = {Euler’s gem:…
Algebra: the Faustian bargain
I came across this great quote from Sir Micheal Atiyah. It is in Barry Mazur’s foreword to Tobias Dantzig’s book Number: the language of science (the 2005 reprinting of the 1930 classic). Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will…
Neat facts from Euler 2010
I had the wonderful honor of being the keynote speaker at the 9th annual meeting of the Euler Society. I spoke today about my book. It is now the end of the second day of this 2.5 day conference. I thought I’d post a few of the many interesting things that I learned. 1. Larry…
David Richeson: Division by Zero 