# Fibonacci clock

Hipster chronometer uses squares inside a golden rectangle to tell the time, and even doubles as a lava lamp.

Don’t you find clock faces quite aggressive, their hands and numbers constantly reminding you of the passing of the time?

If so, this beautiful invention is for you.

The Fibonacci clock lets you know the time more subtly, by changing colours and requiring you do some adding up.

The Fibonacci sequence is the sequence beginning 1, 1 and where each number is the sum of the previous two. Its first five digits are:

1, 1, 2, 3, 5

Philippe Chrétien from Montreal, Canada, noticed that these numbers are all you need to express all the numbers from 1 to 12.

• 1 = 1
• 1+1 = 2
• 1 + 1 + 2 + 3 + 5 = 12

Which means that it is possible to use them to describe the twelve positions on a clock, and therefore tell the time in 5 minute intervals.

Here’s what he did. It is possible to arrange squares whose side lengths are the numbers in the Fibonacci sequence into a rectangle. (This is the famous golden rectangle – here’s a previous post about that).

The squares in his clock have side length 1, 1, 2, 3, and 5. The squares lit up in red tell you the hour, and the squares lit up in green give you the minutes (in multiples of five). A square lit up in blue means it is to be added for both hour and minute. White squares are ignored.

I’ll do the first one below: for hours, you have red 5, red 1 and blue 3. 5 + 1 + 3 = 9 o’clock. For minutes: green 2 and blue 3. 2 + 3 = 5. Then 5 x 5 = 25minutes. So, the time is 9.25.