Two More Impossible Cylinders

Earlier this year I wrote a couple blog posts about reverse engineering Sugihara’s impossible cylinder illusion. I then wrote it up more formally, and it has appeared in Math Horizons (pdf). The example I gave on my blog and in the article was a cylinder that looked like a circular cylinder but like a square cylinder in the…

Measuring Tapes for Circles and Spheres

I’d like to thank Matt Parker for introducing me to diameter tapes (or D-tapes). These are measuring tapes used by foresters to measure the diameters of trees. The forester wraps the measuring tape around a tree as if measuring the circumference, but the scale on the tape is adjusted so that the measurement gives the diameter…

Gabriel’s paper horn

I just returned from the eleventh Gathering for Gardner. One of the many special things about this unusual conference is that the attendees are strongly encouraged to participate in the “gift exchange.” We were each asked to bring a physical exchange item (one for each of the 350 conference-goers) or to submit a written contribution….

2013: the year of pi

A couple days ago I saw this tweet. This is the year of pi. Arctan2 + Arctan1 + Arctan0 + Arctan3 = pi. #pi @centerofmath @MathJesus1 @CutTheKnotMath @maanow @mathematicsprof — John Molokach (@mathemusician_) September 7, 2013 Pretty cool! Let’s see why Two terms are easy to deal with: and But why is One way to…

Bubble diagrams for functions in LaTeX using TikZ

I am teaching Discrete Math this semester (our intro-to-proof course). One of the topics is functions. Not surprisingly my students and I have to draw “bubble diagrams” for functions between finite sets—and we have to include them in LaTeX documents. Rather than simply sketching them in Adobe Illustrator and importing them as graphics, I decided…

Circular reasoning: who first proved that C/d is a constant?

I just uploaded an article “Circular reasoning: who first proved that  is a constant?” to the arXiv. The abstract is below. It is on a topic that I’ve been thinking about and reading about off-and-on for the last year and a half. I’d be happy to hear people’s thoughts, reactions, and impressions. Abstract. We answer the…

Plato’s approximation of pi?

Today I came across an assertion that Plato used as an approximation of . Indeed, it is not a bad approximation: (although it is not within Archimedes’s bounds: ). Not only had I not seen this approximation before, I had not heard of any value of attributed to Plato. I investigated a little further and…

A quick guide to LaTeX

This semester I’ll be teaching real analysis. I am going to have the students type their homework in LaTeX. To make this as easy for them as possible, I will give them a template that is all ready for them to enter their solutions. They shouldn’t have to worry about headers, packages, font sizes, margins,…

Math books for young children

I have a child in first grade and another who will be in elementary school in a couple years. So I’m on the lookout for good children’s books about mathematics. Below is a collection of books that I’ve read or that have been recommended to me. (I got some of these suggestions from people on Twitter.) I’d…

Readers’ response: Euler’s greatest hits

My friend Gene Chase is teaching a history of mathematics class at Messiah College this semester. He asked me if I was interested in giving a visiting lecture in his class in a few weeks. The topic: Leonhard Euler. He said that I could talk about whatever I wanted. Wow, the possibilities! So I was…

Tom Lehrer’s math songs

After writing about some well known people with degrees in mathematics, I was moved to re-listen to some old Tom Lehrer songs on YouTube. I decided I’d post some links to his more mathematical songs here. Enjoy. First, “Lobachevsky,” a song about the Russian mathematician Nikolai Lobachevsky and his discovery of non-Euclidean geometry, which some…

Publish or perish…?

I just received a copy of The Survival of a Mathematician: From Tenure-Track to Emeritus, by Steven Krantz, to review for MAA Reviews. I am only two pages in and I have already found something interesting (on p. xiv, to be precise). It is a hard fact that most American Ph.D. mathematicians write very few…