Chinese Remainder Clock

  • IDEA: To present the number from 0 to 11 that gives the hour, it suffices to specify its remainders after division by 3 and by 4. To present the number from 0 to 59 that gives the minute (or the second), it suffices to specify its remainders after division by 3, by 4 and by 5. This is possible because of the Chinese Remainder Theorem. The mathematics behind the clock is explained in some introductory slides.
  • VISUALIZATION: The vertices of a regular n-gon describe the remainder after division by n. The top vertex corresponds to the zero remainder, the next remainder comes clockwise. The remainders for the hour are in the inner part of the display, those for the minute (or the second) on the outer part of the display. The dial shows the time of your electronic device, so the timezone and the daylight saving time are not an issue.
  • ANIMATIONS: Check out the the digital Chinese Remainder Clock (and a variant of it). See also the IMAGINARY webpage, which includes the analog Chinese Remainder Clock with 7 clock hands, and a digital Chinese Remainder Clock with numbers.

Paper & Slides

The CR-Clock illustrates the Chinese Remainder Theorem.
We prove the Chinese Remainder Theorem in terms of rotations.

App and Animations

  • A simple app for Android, joint work with John Perry, to understand the Chinese Remainder Clock. Available on Google Play. Source files on Github.
    The clock contains various clock designs (Archy/Bubbly/Linus/Ringy/Shady/Vertie).
  • The animations as JavaScript files: analog/digital/digital variant. With a text on how to insert the animation in a webpage.

Further material

  • The exhibit by Markus J. Mühlbauer. Based on an Arduino and with LEDs.
  • The Sage activity, from the book Peering into Advanced Mathematics through Sage-colored Glasses by J. Harris, K. Kohl and J. Perry.

Many thanks to Ted Ridgway (American River College) for suggesting the variant of the digital design.