### Symmetry and the Golden Ratio

Itâ€™s no secret that certain things are â€œmore beautifulâ€ to the eye than others. Much of what we humans perceive as beautiful, or proportional, has to do with shape, balance, and symmetry. Why we have these prejudices I donâ€™t know, but itâ€™s pretty clear that we do have them â€“ to varying degrees. In this article Iâ€™ll explain some theory behind this phenomenon, if you will.

There are innumerable examples of symmetry and balance within our World, and within Mother Nature itself. One reason for the necessity of such proportion is that our World is governed by various laws of physics, gravity being one of them. Without symmetry or balance, things wouldnâ€™t move very well or efficiently, and would result in additional stresses proportional to the imbalance.

Aside from these very crucial physical consequences, symmetry or balance is important for visual comfort. This goes without saying that the visual comfort of which I speak is not only required as a luxury, but to prevent actual physical symptoms such as severe dizziness and nausea. Having said that, I believe there is still plenty of room for innovation and cutting-edge design.

Modern architects have proven that with the right materials and design we can safely construct structures that were previously thought too dangerous â€“ or simply unthinkable. I think many such designs still fall into the â€˜symmetricalâ€™ category, though they may stray from orthodox architectural principles.

The Golden Rectangle

What exactly is so special about this particular rectangle beats me, but apparently thereâ€™s something about its side ratio that makes it extremely appealing to the eye. A given rectangle is a golden rectangle if its side lengths are in the golden ratio. What is the golden ratio (Ï†)? Itâ€™s or approximately 1:1.618. The image to the upper left describes the following relationship:

A unique feature of the golden rectangle is that when a square with a side length equal to the shorter side of the golden rectangle is removed from one end of it, whatâ€™s left is another golden rectangle. Such squares can be repeatedly removed resulting in the same ratio. One can also construct a golden rectangle from scratch with only a compass and a straightedge.

• Start by drawing a normal square of arbitrary size.
• Now draw a line from the midpoint of a side of the square to its opposite corner.
• Use this line as the radius and draw a circle that outlines the height of the rectangle.
• Complete the golden rectangle.