Posts Tagged ‘hinged dissection’

Godzilla’s Dinner Party

August 29, 2008

It’s a little known fact that Godzilla likes to throw dinner parties. Some of these gatherings are formal dinners, with no fewer than four forks, but others are more intimate. Upon occasion Godzilla throws a dinner with only two guests, but then at the last minute a friend drops by and naturally Godzilla invites him to stay for enchiladas with mole sauce (or whatever the evening’s menu). This means that Godzilla has to add a fourth place setting to his triangular table. What to do?

Fortunately, Godzilla’s table is hinged and can turn from an equilateral triangle into a square at a moment’s notice. Allow him to demonstrate. In the mock up below the separate hinged pieces are colored for easy demarcation.

Godzilla prepares by looking at the table.

He slowly starts to separate the pieces:

You can see where the three hinges are (on the outside of the triangle) connecting the four pieces. Godzilla continues to spread them out. There’s a pretty star outline in the center.

He swings those bottom three pieces around…

and up towards to the top

Now it’s starting to look like a square:

And voilà! He’s gotten a square table! The party is saved!

Here’s the final formation in color.

Isn’t that cool?

There’s a slight problem with this design, though, in that there have to be at least four table legs, all close together. Fortunately Greg N. Frederickson designed a triangular table with a large enough piece in the center so that a single pedestal would do, and the six tiny swinging pieces could all be hidden with a linen table cloth. It’s the lead article (“Designing a Table Both Swinging and Stable”) of this month’s College Mathematics Journal. He has some nifty spiff animations here and even more information at the bottom of this page.

For more on these dissections, check out Ivars Peterson’s January 27, 2003 Math Trek column about how chemists were doing exactly the same sort of table spinning as Godzilla (without mentioning him by name, of course) using little plates that would self assemble into different kinds of shapes (although to do the triangle-square hinged switcharoo they had to be connected with thread.)

Time for the dinner party. Pass the enchiladas.