## Animations of swing-hinged dissections of a triangle to a square

The following animations, by Greg Frederickson,
are of swing-hinged dissections of an equilateral triangle to a square that appear in the article:
"Designing a Table Both Swinging and Stable",
by Greg N. Frederickson,

*College Mathematics Journal*, volume 39, number 4 (September 2008), pages 258-266.

Let's start with the swing-hinged dissection
of an equilateral triangle to a square,
illustrated in Figures 1 and 2 of the article.
A simple animation
of a swing-hinged dissection of an equilateral triangle to a square.
This is the version that Henry E. Dudeney demonstrated in 1905,
which was the basis for the design of tables by Howard Eves,
Maty Grünberg, and Joop Van Der Vaart.

Let's move on to the new swing-hinged dissection,
illustrated in Figures 6 and 7.
An animation
of the new swing-hinged dissection of an equilateral triangle to a square.
This version is suitable for the top of a pedestal table.

Finally, let's examine the `little hooks' that can be used in the new swing-hinged dissection,
as illustrated in Figure 9.
An animation
of the new swing-hinged dissection, with hooks, of an equilateral triangle to a square.
Pretty snappy!

Those of you who are interested in animations may wonder why I "chopped up"
my second and third animations. Why didn't I start rotating all of the pieces
at the same time, and stop rotating them all at the same time?
If you are interested, check out
my explanation.

A year after I published my article and first posted this webpage,
I discovered a pleasing alternative to my original dissection.
You can enjoy a
brief description and two animations
of the alternative dissection.

For additional background material on hinged dissections, see:
*Hinged Dissections: Swinging & Twisting*,
by Greg N. Frederickson,

Cambridge University Press, 2002.

If you are interested in building a physical model of one of the swing-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 2008 by Greg Frederickson

and may not be copied, electronically or otherwise,

without his express written permission.

*Last updated September 8, 2009.*