Chinese
Remainder Clock
Idea
The Chinese Remainder Clock (CRC) is a mathematical clock that is based on the Chinese Remainder Theorem. This result tells us, in particular, that to convey a number from 0 to 11 (the hour) it suffices to give the remainder of this number after division by 3 and by 4. Similarly, to convey a number from 0 to 59 (the minutes, or the seconds) it suffices to give the remainder of this number after division by 3, by 4 and by 5.
Visualization
To convey the hour in the CRC, we display the 3-remainder and the 4-remainder of the hour. To convey the minutes (respectively, seconds) in the CRC, we display the 3-remainder, the 4-remainder, and the 5-remainder of the minutes (respectively, seconds). The digital versions of the CRC show those remainders as numbers (for example, the 3-remainder can be either 0,1, or 2). The analogue versions of the CRC convey those remainders through positions of certain objects that rotate with time. For example, the 3-remainder may correspond to the positions at the vertices of an equilateral triangle (for the 4-remainder and the 5-remainder we would have instead a square and a regular pentagon respectively).
Settings
12/24-hour Mode
Visibility Settings
Color Settings
Hours
Minutes
Seconds
References
Paper & Slides
The CR-Clock illustrates the Chinese Remainder Theorem.
We prove the Chinese Remainder Theorem in terms of rotations.
- The Chinese Remainder Clock in The College Mathematics Journal.
- Introductory slides about the Clock (and their source file).
- Slides explaining the Chinese Remainder Theorem with rotations (and their source file).
- Tutorial about the Clock (and their source file).
Further material
- The exhibit by Markus J. Mühlbauer. Based on an Arduino and with LEDs.
- The IMAGINARY webpage, which includes the analog Chinese Remainder Clock with 7 clock hands.
