Here’s a nice shape, somewhere between a circle and a square, that might be an interesting design break from those standard forms.
Mathematically, it is a superellipse. The formula is
The shape of the figure can be varied with the selection of the parameter, a. Math fans will recognize that, for a=2, this is the formula for a circle.
If a is close to 2.0, the figure will look more rounded. As a grows larger than 2.0, the shape becomes squarer, with rounded corners and a gentle curve along the sides.
The illustrations show squarish shapes. Rectangular forms can be obtained by scaling either axis.
Edited 4/27/2003 6:30:51 PM ET by Donald C. Brown
Replies
Just an offhand observation, if you set a = 1 you get a square. Evidently the shape approaches a square (as shown) as the value of a approaches infinity.
Cheers, Chris
If a is less than one, the figure is interesting in the other direction.
View Image
Thanks, Rainman.
Donald --
Yes, the superellipse is an interesting shape. I've built dining tables with it, and it works very well -- almost magically well. I set your parameter a to about 2.8, and make the table more rectangular than square. Compared to a true rectangular table, it has darn near as much seating capacity, yet nobody is stuck out on a corner. Compared to an ellipse, nobody gets stuck sitting at an end that is too pointy. When I watch the conversational dynamics around a superellipse dining table, I see that everybody seems included, no matter whether there are two people at the table, or it is full.
Jamie
One more thought --
A Danish mathematician named Piet Hein designed traffic roundabouts and furniture using superellipses in the fifties and sixties. Surf around, and look in history books, and you can find some of his work.
A Danish mathematician named Piet Hein ...
That's exactly where I started. Martin Gardner, who used to write the recreational math column for Scientific American, mentioed Piet Hein a number of times during the period to which you refer. I don't know why that stuck in my mind, but when I was looking for a shape more pleasing than a rectangle for just the application you mention, I used that name for my search.
There was an article in Woodwork magazine on this topic approximately 2 years ago. I would have to check my back issues to find out exactly which issue it was in.
I looked it up; it's in the October 2000 issue.
Edited 4/29/2003 7:53:43 AM ET by BenM
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