Using wikis in mathematics classes

Wikipedia describes a wiki as a website that allows the easy creation and editing of any number of interlinked web pages… [Wikis] are often used to create collaborative websites, to power community websites, for personal note taking, in corporate intranets, and in knowledge management systems. I have used wikis in three of my classes: two…

More about the neat calculator trick

Yesterday I wrote about a neat calculator trick that I had just learned. We saw that if the calculator was set to degree mode, then times a high enough power of 10 is approximately . A commenter named Robert suggested looking at the difference between this approximation for and itself. He remarked that the error…

The math behind a neat calculator trick

[Update: after you read this post, read my follow-up post.] I received an interesting comment on yesterday’s blog post from Nemo. It was a cool calculator trick that I’d never seen before. Nemo wrote: Reminds me of my favorite calculator trick. Set your calculator to degree mode (NOT radians). Type in a bunch of 5’s:…

Interesting approximations using trigonometry

Today on Twitter John D. Cook, writing as @AlgebraFact, posted the following tweet: In radians, sin(11) is very nearly -1. (It happens to be -0.9999902…) I thought that was awesome! So, I (@divbyzero) replied that cos(333) is approximately 1. (It is 0.999961…) Then @michiexile chimed in, pointing out that cos(355) is closer to -1 than…

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…

Posting items to my blog using wplatex

This blog post is aimed at other mathematicians who write on WordPress blogs. I’m writing this blog post completely in TexShop on my Mac! Recently I discovered that Eric Finster at Curious Reasoning wrote a Python script called wplatex that converts LaTeX documents to HTML that is WordPress compatible. Then it posts the files directly…

What is the cardinality of the Euclidean topology?

I’m teaching topology this semester. The students are looking at different topologies on the real number line. For homework I asked them to think about which topologies are “the same” (if any) and which are “different,” and why they thought that was the case. We haven’t yet talked about continuous maps or homeomorphisms, so I…

Proof that pi is irrational

Have you ever seen the proof that is irrational? If not, I highly recommend heading over to The Math Less Traveled. Blogger Brent Yorgey just posted the last of his six part series in which he gives Ivan Niven’s easy-to-follow 1947 proof of that famous fact. The proof uses only basic calculus.

Three applets illustrating parametric curves

In my multivariable calculus we’re talking about parametric curves. I’m using this applet for displaying parametric curves. You can use predefined curves or enter your own. Although the applet is on my web page, it was created by Marc Renault, a friend who teaches down the road at Shippensburg University. I only tweaked it slightly when…

Why do mirrors reverse right and left but not up and down?

[I apologize to those of you who have been reading my blog for more than a year. I’m reposting something I wrote last year at this time. I was then, and am now, teaching Calculus III, and we just finished discussing the cross product. I ended the conversation by telling my classes how the cross…

Three applets for linear algebra or multivariable calculus

This semester I’m teaching two sections of Calculus III (multivariable calculus) and I happen to be teaching the first four weeks of Linear Algebra. The first couple weeks of both courses cover properties of vectors in Rn. (Of course, just to confuse the instructor and the students who happen to be in both classes, the…

Division by Zero listed as one of 50 Best Blogs for Education Leaders

This morning I was pleased to discover that my blog appears on OnlineUniversities.com‘s blog in their list of the 50 Best Blogs for Education Leaders; it was one of the five blogs listed in the Subject Specific category. What a nice surprise. I’m very honored for the recognition! This is the first I’d read their…