## 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.

Text and animations are copyright 2006-2007 by Greg Frederickson

and may not be copied, electronically or otherwise,

without his express written permission.

*Last updated December 12, 2007.*