Animations of some wild twist-hinged dissections

The following animations, by Greg Frederickson, are of twist-hinged dissections that appear in the article:

"The Heptagon to the Square, and Other Wild Twists", by Greg N. Frederickson,
Mathematical Intelligencer, volume 29, number 4 (2007), pages 23-33.

Let's start with the twist-hinged dissection of an equilateral triangle to a square, illustrated in Figures 6 and 7 of the article.

A simple animation of an equilateral triangle to a square, in which I twist each hinge one at a time.

A more interesting animation of that same twist-hinged dissection of an equilateral triangle to a square, in which I twist a pair of hinges simultaneously. Each such pair of twist hinges corresponds to a swing hinge, so that this animation more closely simulates an animation of the original swing-hinged dissection.

Here are animations of some of the loveliest twist-hinged dissections in the MI article:

Regular heptagon to a square (illustrated in Figure 9).

Regular hexagon to a square (illustrated in Figure 11).

A {12/2}-star to a square (illustrated in Figure 17).

Regular pentagon to an equilateral triangle (illustrated in Figure 23).

An {8/3}-star to a regular hexagon (illustrated in Figure 29).

For additional background material, see:

Hinged Dissections: Swinging & Twisting, by Greg N. Frederickson,
Cambridge University Press, 2002, pages 228-256.

If you are interested in building a physical model of one of the twist-hinged dissections in the article, but are puzzled by what the angles and dimensions should be, please send me a message ( gnf at cs.purdue.edu ) and I'll work them out for you.