The golden ratio has spawned a beautiful new curve: the Harriss spiral

Alex Bellos in The Guardian:

Harriss was overjoyed when he first saw the spiral because it was aesthetically appealing – one of his primary aims was to draw branching spirals like you might find in Islamic art or the work of Gustav Klimt. But he was particularly delighted because he arrived at the spiral using a very simple mathematical process.

“It’s not hard to make something that no one has seen before,” he said. “It’s more difficult to make something mathematically satisfying that people haven’t seen before.”

His first concern was that maybe someone else had had, in fact, drawn the spiral “One thing about mathematical discoveries and mathematical art is that even if the process is completely new there is no guarantee that someone else has not already explored it.”

It turned out that the ratio 1.325, which gives you the rectangle that creates the Harriss spiral has been written about – it is known as the “plastic number” – but Harriss could find no previous drawings of the spiral. (In fact, the ratio is a number that begins 1.32472… and carries on forever).

More here.