In the late 1990s, Erik Demaine, Martin Demaine, and Anna Lubiw proved that any pattern made from straight line segments in the plane—connected or not—can be cut out of a piece of paper by first making some strategic folds and then making a single cut. This is the now-famous Fold-and-Cut Theorem. (See Erik Demaine’s website,…
Tag: origami
Folding a Cardioid
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…
Tales of Impossibility: Now Published!
I’m very excited to announce that my new book, Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019), is now available! (OK. It was published about a month ago, but I am just now getting around to blogging about it.) Like my previous book, Euler’s Gem (Princeton University…
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…
Angle trisection using origami
It is well known that it is impossible to trisect an arbitrary angle using only a compass and straightedge. However, as we will see in this post, it is possible to trisect an angle using origami. The technique shown here dates back to the 1970s and is due to Hisashi Abe. Assume, as in the…
Twitter and Origami
Twitter is amazing. Two nights ago I watched the PBS documentary on origami, Between the Folds. Yesterday morning when I got to my office I made the following post on Twitter: In the next 12 hours I was flooded with suggestions, comments, and links. Here are some of the book titles and links that people sent…
Folding a golden rectangle
Recently I wrote about the mathematics of cutting and folding paper and about the golden ratio, . Here’s a video that brings these two ideas together. We see how to create a golden rectangle (a rectangle for which the ratio of the sides is ) by folding a piece of paper. [via Anthony Brand’s maths…
Cutting and folding paper
Inspired by Chaim Goodman-Strauss’s recent video about symmetries, paper snowflakes, and paper dolls, I decided to post a few other paper-related videos. First is a video showing some cutting tricks for a Möbius strip. I show this to my topology class, then have them play around with Möbius strips—twisting them various numbers of times and…
David Richeson: Division by Zero 