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The Golden Rectangle

An animation showing how removing a square from a golden rectangle leaves another, smaller golden rectangle.

Brief Explanation

The Golden Rectangle is a rectangle with a special shape. It has been known about since antiquity, and is thought by some to have proportions most pleasing to the eye. (Although it is apparently not true that the Parthenon’s dimensions were based on it.) Its defining property is this: if you slice a square off one side of a golden rectangle, the remaining rectangle will have the same proportions — the ratio of long to short side — as the original.

first steps

This page shows how that process can be repeated to produce a series of golden rectangles. The question is: does your mind do this sort of thing unconsciously? Do we perceive all the nested golden rectangles at some level?

Try It Yourself

To subdivide the golden rectangle, click here. There are seven steps in all.
To start again, click here.


As you can see, each nested rectangle also is golden — that is, it has the same proportions as the large starting rectangle. In addition, the “spiral” line (it’s not an exact spiral, but a combination of circular arcs) is an approximation to a true golden spiral.

The next pages will explore how to calcuate the unique ratio of sides that makes a golden rectangle, and show how it is connected to recursion and fractals.

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