Cyclic numbers are special types of numbers that exhibit a unique property when multiplied by integers. When you multiply a cyclic number by 1, 2, 3, and so on, the results are simply rotations of the original number. The most famous example of a cyclic number is 142857, which is derived from the fraction 1/7. These numbers are closely related to the concept of repeating decimals and number theory. Cyclic numbers are fascinating because they reveal patterns in multiplication and can be used to explore the properties of numbers in a mathematical context.