## Pythagoras Clock #Clocks

Thanks to Julian Richardson for sharing his great clock project with us! Read more at his blog here.

The traditional clock shows the hour divided into 12 periods of 5 minutes, 6 periods of 10 minutes, 4 periods of 15 minutes ( a quarter of an hour ), 3 periods of 20 minutes, and 2 periods of 30 minutes (half an hour). This neat divisibility is a consequence of the factorizations of the number of hours in a day and minutes in an hour: one day = 12 hours = 3*4 hours – resulting in integer factors of 2, 3, 4 and 6 hours. One hour = 60 minutes = 3*4*5 minutes – resulting in integer factors of 2, 3, 4, 5, 6, 10, 15, 20, 30 minutes. If there were 61 instead of 60 minutes in an hour, then half an hour, a quarter of an hour – none of these would correspond to a whole number of minutes.

There is something else special about these numbers: 3, 4 and 5 make up the least Pythagorean triple: a right angled triangle can be drawn with sides 3, 4, and 5 units long.

A few years ago, I designed the Pythagoras Clock, based on this coincidence.

The clock is powered by an Atmel ATMega168. The clock display is made of laser cut acrylic, housing 19 colored LEDs laid out in two intersecting Pythagorean triangles.

The two lines in the upper right corner – excluding the diagonal – represent fractions of a day, and the three lines in the bottom left corner plus the diagonal, represent fractions of an hour.

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