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 from a single cylinder of wood. These four helices were cut by Steve Garrison, who was the first to think of this, as far as I know.
Pleats created in pieces of fabric to create geometric patterns are known as Shadowfolds. Here’s how to fold your own.
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.
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 easy to make many kinds of sphericons, with different starting polygons. Here is one based on a star.
Make these lovely, stuffed stellated dodecahedron models, in knit or crochet.
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 divided into squares of distinct integer sizes.
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 to make star-like geometric forms.
