It is well known that we can make a cardioid by drawing straight lines inside a circle. Simply choose one point on the circle’s boundary to be the base point. Then, connect points on the circle to the points twice as far away from the base point (measured along the circumference). If there are n…
Tag: Math
Drawing a Celtic Knot
I decided to put together some activities for a gathering of math and computer science majors—puzzles, math crafts, etc. One of them was to draw a Celtic knot. I decided to write up a handout with the instructions. I thought I’d post it here. Enjoy! Here’s a printable pdf of the handout and the diamond-shaped…
Make a Real Projective Plane (Boy’s Surface) out of Paper
I am teaching an undergraduate course in topology. We are now looking at what we get if we take a square and glue the sides together. (These are called identification spaces.) We are assuming that our spaces are made out of very stretchy rubber. So, if the space begins as a square, we could, for instance,…
The Magnificent Möbius Band
As I write this blog post, we are all either struggling with the impact of the COVID-19 virus or waiting nervously as cases start to rise in our area. I am currently teaching remotely. My college students are scattered around the globe, and we are interacting through various online methods. This semester I am teaching…
BraidTiles—A Mathematical Braid Puzzle
We can view braids mathematically as n strings hanging from a horizontal bar. Each piece of string runs downward and can cross neighboring strings. In the 1920s Emil Artin observed that braids of n strings form an algebraic group. To “multiply” two braids, we append the bottom of one braid with the top of another braid. The identity element in this group…
My First Crossword Puzzle
I recently discovered Phil, an HTML5 crossword puzzle maker (here it is on GitHub). I’ve always wanted to make a crossword puzzle, but it seemed overwhelming. But with Phil, I found it fun and addicting! So, here is my first creation. It has a mathematical theme. I’ve enjoyed solving crossword puzzles off and on over…
Math Crafts: Salt Designs, Newton Snowflakes, Fractal Christmas Trees, Paper Pentagons, and Flip Books
I have had a crafty late fall and early winter. I’ve been good about posting my crafts on Twitter, but not so good at blogging about them. So, I’ve collected them all and will share them all here in one blog post. The Geometry of Salt I came across this neat pdf by Troy Jones…
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….
David Richeson: Division by Zero 