Good activity for an Introduction to Proofs class

I just read this post at Futility Closet. (Spoiler: Don’t click the link unless you want to know the punchline.) Perhaps the result is well known, but I hadn’t seen it before. The post made me think of a neat project for an “Introduction to proofs” class. I’ll have to save it for the next…

Editing a Very Poorly Written Proof

I’m teaching Discrete Math this semester. Discrete Math is our college’s “introduction to proofs” class. We spend a lot of time talking about and practicing proofwriting. In earlier blog posts I shared my “Nuts and Bolts of Writing Mathematics” and an “editing checklist” that I give to them. Yesterday, I gave them an example of…

Tangent lines to the sine function with rational slope

Today I was wondering the following thing (I won’t bore you with how I ended up with this question): Are there any rational values of for which the line is tangent to the graph of Clearly the answer is yes: But my gut feeling was that this was the only such After some head scratching,…

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….

Undergraduate Math Bloggers

I was interested seeing how undergraduate math students used blogs (and related platforms, like Tumblr). So I posted a call on Google+ and Twitter: I'm looking for mathematics blogs written by undergraduate students. Any recommendations? I'll retweet/repost them as they come in. — Dave Richeson (@divbyzero) February 17, 2014 I received quite a few links. I’m looking…

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…

Using a kayak to measure the perimeter of a lake

I’m on vacation this week on a lake in northern Michigan (hold up your right hand, palm toward you, point at the first knuckle of your middle finger—that’s where I am). Yesterday I paddled around the perimeter of the lake in a kayak. On a whim I brought my GPS-enabled phone. My route is shown…

Countability of the rationals drawn using TikZ

I’m continuing my exploration of TikZ (here is my first post about TikZ). I will be showing my Discrete Math class how to “count” the positive rational numbers. (See this old blog post for more information about countable sets.) I used TikZ to create the picture below. Here is the source code for this figure. If you click…

Greatest living mathematician and expositor?

On Twitter I posed the following question: I got a great repsonse. Here is the complete—unedited—list of names (in alphabetical order). Micheal Atiyah Art Benjamin Andrea Bertozzi Manjul Bhargava Joan Birman Bela Bollobas Stephen Boyd María Chudnovsky Fan Chung John H. Conway Ingrid Daubechies Keith Devlin Marcus du Sautoy Jordan Ellenberg Joe Gallian Rob Ghrist…

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…

Interview on Wild about Math!

I had a very nice conversation with Sol Lederman (of the Wild about Math! blog) on his “Inspired by Math” podcast series. Check it out and be sure to check out his other podcast episodes.