Sixty

The sixty (60) is the natural number that follows fifty-nine and precedes sixty-one.

Mathematical properties

• It is a number composed of several auxiliary numbers and have the following divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. As the sum of its dividers is 108 /2005 60, it is an abundant number. It is also a number with more dividers than each of the dividers of all its dividers.
• This number is the sum of a pair of twin cousins (29 + 31), a number between two twin cousins (59 and 61), as well as the sum of four consecutive cousins (11 + 13 + 17 + 19).
• The inner angles of an equilateral triangle measure 60 degrees each, adding up to 180 degrees.
• The Babylonian numbering system had a base of sixty; a numbering system with the base sixty is called a sexagesimal numbering system.
• In geography the sixty is an equally important number: the circumference of the Earth is 360 degrees, that is, six times sixty; each degree is divided in sixty minutes, and every minute in sixty seconds. Similarly, in time measurement every hour is divided into sixty minutes, and every minute in sixty seconds. Just like a heritage of the Sumerians, who used the division of circumference in 360 degrees, the year in 12 months, the day in 12 hours and the night in the same amount. It also comes from them 7 days a week.
• It is the value of a cathet of a rectangle triangle that has by hypotenuses 61 and 11 by the other cateto. It is an example of primary primitive pythagorean.
• The product of the elements of a pythagorean tenare is always a multiple of 60. In other words: the product of the sides of a diophantine rectangle triangle is always a multiple of 60.
• The number 60 can take the form algebraic mn (m2 - n2)= m3n - mn3, for m = 4 and n = 1. When these positive integers m and n are odd, cousins between themselves and m  n, the number mn (m2-n2) is called "Congruent number of Fibonacci". The minor is 24. (Liber Quadratorum: The Book of Square Numbers, 1225)
• It's a Harshad number.

Features

• The origin of the popularity of the number 60 must be sought in that it is the result of multiplying 5 by 12. Already since ancient times the 12th was an important number, resulting from the times the Moon turns the Earth in a year. For its part, the 5 was equally important, since it corresponds to the fingers of one hand, which the primitive peoples used to count.