> > I'd like to know what answers one would get by asking people which > shape of rectangle they find most pleasing, although since this > would only take a few minutes it shouldn't count as a classroom > project. My guess is that almost everyone would choose something > "squatter" than the golden rectangle by quite a long way; probably > less than root2 : 1. >
- - - - - - - - - - - - - - In 1995, Carrie Milne, then a student at Alma College in Michigan, conducted an experiment on "Preference for the Golden Rectangle." Subjects were asked to "draw" on a computer screen a rectangle that seemed most pleasing to them. Using a mouse they could vary the base and height of the rectangle until they saw it as being just right. Carrie found that most persons preferred rectangles with ratios of base to height less than phi. Preferences clustered around 1.18:1, 1.38:1, and 1.53:1. (Carrie presented her results, which are consistent with Antreas' conjecture, at the Pi Mu Epsilon student conference at Miami University, Sept. 1995.)
On the other hand, George Markowsky (_College Mathematics Journal_, 23:1 (January, 1992) reports on his own "informal experiments," asking people to select the "most pleasing rectangle" from a collection of 48 rectangles (all visible at once). He claims that "the most commonly selected rectangle is one with a ratio of 1.83."