At IPP20 in August 2000, Joop Van Der Vaart told me that he had had a hinged triangle-to-square table built, of the sort that Howard Eves described. He had the craftsman Jan de Koning build the table. He also said that he had seen a promotional toy based on the hinged triangle-to-square dissection of Henry Dudeney. I mentioned that I would very much like to see photos of the table and the toy, because of the featured role of the hinged triangle-to-square dissection in my book. A big thank-you to Joop for taking the pictures and sending them to me!
First, the table as seen from above, with the pieces swung out:
the pieces swung to form the triangle:
and the pieces swung to form the square:
Next, the table flipped over, so that you can see how the legs are positioned. There are seven legs, one at each corner of the square and at each vertex of the triangle:
A sideways view of the table, formed into the square:
A sideways view of the table, formed into the triangle:
In 2006 I designed a different hinged table, one with more pieces (seven rather than four), but with one very large piece and the rest small.
I have posted a webpage containing animations of swing-hinged dissections of triangular to square table tops.
These swinging tables are discussed in my article, "Designing a Table both Swinging and Stable",
College Mathematics Journal, vol. 39, no. 4 (September 2008), pp. 258-266.
Finally, two views of the promotional toy distributed by ABN AMRO, a global banking group, ranked fifth in Europe and sixteenth in the world.
It's wonderful to discover that bankers, or at least their publicists, have excellent taste!
Photos courtesy of Joop Van Der Vaart.
All else copyright 2001, Greg N. Frederickson.
Permission is granted to any purchaser of
Hinged Dissections: Swinging & Twisting
to print out a copy
of this page for his or her own personal use.
Last updated July 10, 2009.