mondrian-golden-ratio Over the past two weeks our Euclidean Geometry group has been investigating the “Golden Ratio”. It’s the solution to an equation that allows us to construct a regular pentagon using only a compass (for drawing circles) and a straightedge (for drawing lines) — you can read a lot more about its geometry here.

Part of the construction involves the square root of 5, which we can get from the Spiral of Theodorus:400px-Spiral_of_Theodorus.svg

The Golden Ratio is a number and it’s intimately related to the Fibonacci series. It has many amazing properties, making it a favourite among mathematicians (here are some, for enthusiasts only). The way this strange number arises from a simple set of drawing constraints is surprising to say the least. Sometimes the simplest starting-points really can give rise to mystery and complexity.

Then there are the alleged connections with art practice. As Keith Devlin explains in this lecture (try here or here if you’d rather read), some of these are pretty fishy.  In that video Devlin uses a simple experiment to demonstrate that people don’t “prefer” Golden Rectangles over other rectangles, as people sometimes claim.

Some twentieth century artists and designers have explicitly used the Golden Ratio in their work, most famously Le Corbusier. Watch out, though, for bogus claims even coming from the creators themselves. For example, Twitter’s Creative Director is reported to have claimed that its page layout is based on the Golden Section, but the picture used to “prove” this fact doesn’t seem to show much agreement between the layout and the overlaid geometry at all!