Rectangles

Rectangles are rather an interesting shape, no?

Mostly no, it is true. But they are rather fundamental to most art, architecture, and sense of proportion.

For example, the Golden Ratio...

<math>\varphi = \frac{1 + \sqrt{5}}{2}\approx 1.618\,033\dots\,</math>

...is often claimed to be the most pleasing rectangle to the human eye, with it's proportions to be found everywhere both in nature and human achievement (esp classic architechture)

Now I wonder how that varies significantly from other simple proportions you could construct... (say, pi/2) when it really comes down to it...

<math>\frac{\pi}{2} \approx 1.570\,796\dots</math>

...that is less than 3% smaller.

As a personal note, I much prefer the A-series of paper sizes (Lichtenberg rectangle)...

<math>\sqrt{2} \approx 1.414\,213\dots</math>

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So, have any studies ever been done to actually poll people on their most favourable-to-the-eye rectangle?