As the editor-in-chief of the Make: website, I got to help develop column ideas and work with some amazing contributors. One of these was the brilliant George Hart (father of Vi Hart) from the Museum of Mathematics. After George left the museum, Glen Whitney took over the column. They both did an amazing job at demonstrating mathematical concepts in the most entertaining ways, using everyday objects and maker-made creations. You can see all of the installments of the series here.
Here is the briefest of samplings. The column ran (on and off) for eight years.
A mathematical haircut makes an unambiguous statement to the world that you love math. Here, Nick Sayers is sporting a rhombic coiffure with interesting geometric properties.
The obtuse angles of each rhombus meet in groups of three, but the acute angles meet in groups of five, six, or seven, depending on the curvature. In the flatter areas, they meet in groups of six, like equilateral triangles, and in the areas of strong positive curvature they meet in groups of five, but in the negatively curved saddle at the back of the neck, there is a group of seven.
To make your own, Nick suggests you use a rhombic paper template starting at the crown, work outwards, and make aesthetic decisions about the 5-, 6-, or 7-way joints depending on local curvature. This instance of the design was cut by Hannah Barker after a test version a couple of months earlier by Summer Makepeace.
We've seen mathematical pencil constructions in past Math Mondays columns. (Why go to the hardware store to buy dowels with all those shiny pencils just sitting there in the office supply cabinet waiting for someone to make things with them?) Here's a lovely new design by Cory Poole. It is a five-pointed star assembled from eighty pencils.
There are five identical 16-pencil units around a central axis. Two units are shown below, before assembling. Each has the form of a hyperbolic paraboloid based on a four-edge cycle from a regular tetrahedron.
If you'd like to make your own, Cory provides step-by-step construction instructions.
Speaking of office supplies, a box of mailing tubes showed up in our Museum of Mathematics office and I couldn't resist making a geometric construction. All you need to make your own copy are thirty tubes and sixty rubber bands. All the tubes are surrounded similarly. Each touches four others, approximately outlining an icosidodecahedron.
I showed this to Keith Hoffman and he made the same structure from 510 Lego studs and 60 tiny clear rubber bands.
What can you use to make this structure?
After last week's column on mathematical quilts, I thought I should continue in the fiber arts category with mathematical objects that can be made by crochet. Matthew Wright at the University of Chicago has crocheted some beautiful Seifert surfaces, shown below. These are (approximately) the form that a soap film would take if you made a knot out of wire and dipped it in soap solution. The first is based on a trefoil knot, made from a continuous path of blue yarn, with a red Seifert surface spanning it.
The example below is based on the Borromean rings — three separate loops which are locked together. The black surface shows the intricate shape of the soap film that would form between them.
If you would like to crochet your own Seifert surfaces, you can explore an infinite variety to choose from with the SeifertView program.