Regular Number
Regular numbers are numbers that evenly divide powers of 60. As an example, 602 = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60. Thus, they are also regular numbers.
The numbers that evenly divide the powers of 60 arise in several areas of mathematics and its applications, and have different names coming from these different areas of study.
- In number theory, these numbers are called 5-smooth, because they can be characterized as having only 2, 3, or 5 as prime factors. This is a specific case of the more general k-smooth numbers, i.e., a set of numbers that have no prime factor greater than k.
- In the study of Babylonian mathematics, the divisors of powers of 60 are called regular numbers or regular sexagesimal numbers, and are of great importance due to the sexagesimal number system used by the Babylonians.
- In music theory, regular numbers occur in the ratios of tones in just intonation, also called 5-limit tuning for this reason.
- In computer science, regular numbers are often called Hamming numbers, after Richard Hamming, who proposed the problem of finding computer algorithms for generating these numbers in order.
Read more about Regular Number: Number Theory, Babylonian Mathematics, Music Theory, Algorithms, Other Applications
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