[ExI] fibonacci clock

William Flynn Wallace foozler83 at gmail.com
Fri Nov 10 14:34:26 UTC 2023

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 <http://basbrun.com/> 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 <http://en.wikipedia.org/wiki/Golden_rectangle>).
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.

The first one below goes like this:
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 = 25 minutes.
So, the time is 9:25

Some more examples:

The clock in action:

It has a lava-lamp mode too, when you just want to forget the time for a

Cool, huh? :)

1) Interested people can support, and buy this cool, nerdy invention from
this Kickstarter page
2) Vaibhav Jalan <https://www.quora.com/profile/Vaibhav-Jalan> has made a
cool website version <http://vjthebot.github.io/fibclock/> of this. Do
check it out.
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