I once read about this architect who had a project underway where a large open area was to be provided with vertical columns. He decided that the usual circular column cross section was not esthetically pleasing and that he wanted to use something else, but what that something else would be was elusive. Therefore, he sought the assistance of a consultant, in this case, a professor at a nearby university.

The professor came up with something right away.

The equation of a circle is x² + y² = Radius² for which the exponent of each variable is "2". The professor said to instead use the equation x^{1.5} + y^{1.5} = Radius^{1.5} for which the cross section looks like this:

As it happened, this form for the column appealed to the architect very much, but what really surprised him was that trying other exponent numbers didn't lead to anything that was any more visually pleasing:

Clearly, the exponent "0.5" could be downright dangerous to passersby. The exponent "1" just doesn't look nice and might be hazardous in its own right.

Of the exponents greater than unity, that professor, the consultant, seemed to have hit the right answer immediately.

While I don't really have the time or inclination to plot it, I wonder if the "Golden Rectangle" ratio (1:1.618, roughly) might be even more esthetically pleasing.

Posted by: Larry Rachman | August 25, 2011 at 11:40 AM

Hi, Larry.

I just ran the calculation and plot for the exponent value as the Golden Mean = 0.5*(1+sqrt(5)) and it doesn't really look all that different from the 1.5 value.

It's on its way to you by e-mail and if anyone else would like to see it, just e-mail me at ambertec@ieee.org.

John

Posted by: John Dunn | August 25, 2011 at 06:46 PM