The biography of Augustus De Morgan in The MacTutor History of Mathematics Archive ends with the following interesting tidbit. De Morgan was always interested in odd numerical facts and writing in 1864 he noted that he had the distinction of being years old in the year (He was 43 in 1849). Anyone born in 1980…
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…
Polya on Euler
One of my computer science colleagues sent me this quote from Polya about Euler. This is usually something I’d to post on Twitter, but it is too long. So I thought I’d reproduce it here. …among old mathematicians, I was most influenced by Euler and mostly because Euler did something that no other great mathematician of…
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…
David Richeson: Division by Zero 