# Modular Multiplication on a Circle

Modular Multiplication on a Circle

Multiply the positive integers by 3 (mod 10) to get the repeating sequence . This Demonstration connects the starting values to the ending values for a chosen modulus and multiplier .

3,6,9,2,5,8,1,4,7,10,…

1,2,3,…

1k,2k,3k,…

k

With multipliers of 2, 3, and 6, cusped epicycloids develop—the cardioid, nephroid, and ranunculoid. Other patterns develop with other moduli and multipliers.