Fibonacci Time

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This Demonstration shows a clock based on time expressed using the first five Fibonacci numbers: 1, 1, 2, 3, and 5. 

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Every integer from 1 to 12 can be expressed as the sum of a subset of those numbers, so that one can express hours and minutes in increments of 5 minutes.

The clock itself is a rectangle divided into five squares with side lengths equal to the first five Fibonacci numbers.

To tell the time, a color convention is needed: red is for the hours, green for the minutes, blue for both. The white squares are to be ignored. To read the hour, add up the values of the red and blue squares. To read the minutes, add up the values of the green and blue squares and multiply by 5.

The conversion of hours or minutes to "Fibonacci sums" is not always one-to-one, as an integer between 1 and 12 can be expressed by different sums. For example, 5 can be expressed as , , or and 10 can be either or