By George Hart for the Museum of Mathematics Here is a wide variety of mathematical beadwork structures by Horibe Kazunori. Looking closely at one example, you can see how the surface curvature depends on the structure. Generally, six-sided cycles correspond to an infinite tessellation of hexagons, which makes a flat... Read more »

Math Monday: Nested Helices

If you want to make a screw of wood, the first tool you would think of is a lathe. But you can also make a screw on a scroll saw. In fact, I was stunned to learn of a surprising technique for using a scroll saw to make nested screws... Read more »

By folding a pleat in piece of fabric, you make one layer into three layers. By choosing the width and direction of many pleats, you can make geometric patterns. Chris Palmer has raised this to an artform with works that he calls Shadowfolds. Read more »

Math Monday: Coffee Stirrers

Nick Sayers enjoys making geometric constructions from unusual materials. Here's an organic-looking sculpture he made from 630 coffee stirrers, with "blobs" protruding in the twelve directions of a dodecahedron's faces. Read more »

Math Monday: Star Sphericon

A sphericon is a shape that you get by: (1) rotating a symmetric polygon about a mirror axis to get a solid of revolution, (2) cutting the solid into two equal pieces, and (3) putting the pieces back together differently. With a lathe or a 3D printing machine, it is... Read more »

Math Monday: Knit or Crochet a Dodecahedron

By George Hart for the Museum of Mathematics If you knit, here’s a stuffed, dodecahedral thing—I don’t know quite what to call it—a toy, a pillow, a mathematical model? The shape is based on twelve 5-sided units like a dodecahedron. But they bump out, so the form is more like... Read more »

Math Monday: The Squared Square

If you are a cabinet maker, geometry is essential to all the lengths and angles that you calculate. The cabinet shown here goes further and presents the solution to a rather difficult dissection problem. This is the simplest perfect squared square. The entire area is a square and it is... Read more »

Math Monday: Cardboard Catenary Arches

By pleating a square sheet of paper with a pattern of concentric squares, one can fold a saddle shape that mathematicians call a hyperbolic paraboloid, sometimes nicknamed a hypar. Erik Demaine led a workshop at a recent Museum of Mathematics event where he showed how multiple hypars can be assembled... Read more »

Math Monday: Fold Your Own Hyperbolic Paraboloids

By George Hart for the Museum of Mathematics By pleating a square sheet of paper with a pattern of concentric squares, one can fold a saddle shape that mathematicians call a hyperbolic paraboloid, sometimes nicknamed a hypar. Erik Demaine led a workshop at a recent Museum of Mathematics event where... Read more »

Math Monday: Stained Glass Polar Zonohedron

Stained glass can be used to make many mathematical forms. One very beautiful shape is the polar zonohedron. Hans Schepker made this three-foot diameter example from hundreds of pieces of stained glass. Read more »

Math Monday: Cut and Fold Escher

By George Hart for the Museum of Mathematics The Dutch graphic artist M.C. Escher has inspired many people to create mathematical artwork.  This elegant cut-and-fold paper model of Escher’s famous lithograph, Relativity, is a virtuoso homage to Escher’s genius. Bryan Peele designed this construction, which is cut from a single... Read more »

Math Monday: Pencil Star

By George Hart for the Museum of Mathematics 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... Read more »