Clock Arithmetic

Number Theory · Axiom Academy

Discover how time-telling reveals a hidden mathematical universe. Move the slider to add hours to the clock. What happens when you go past 12? Try adding different times together. Notice what happens when the sum goes past 12. Click on different examples to see how clock arithmetic works with various numbers. Choose any number and see where it lands on a clock (mod 12). Clock arithmetic is formally called modular arithmetic . It's a complete number system where numbers "wrap around" after reaching a certain value (the modulus). Modular arithmetic powers cryptography, computer science, music theory, and even calendar calculations. The RSA encryption protecting your online data relies on modular arithmetic! Modular arithmetic follows its own rules for addition, subtraction, and multiplication. You can even solve equations in modular arithmetic, opening up entirely new areas of mathematics like number theory and abstract algebra.

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