Sept 13 Why Base 60?

60 is a number with many factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Contrasting it with 10, which only has 4 factors. The large number of factors makes base 60 calculations more flexible in many situations, especially when it comes to divisions or fractions. For example, it's much easier to express a third in a base 60 system (as 20) than in base 10 (which results in an endless repeating decimal: 0.333...). So getting rid of the notion of repeated values for some rationals may allow people to think more clearly and focus more on the value of a third, rather than the repetitions. 

The factors of 60 are used in many places in time and geometry. The number of degrees in a circle is 360, which is very similar to the number of days in a year 365). 60 degrees is also the angle of a special right triangle. The number of days in a year is defined by the orientation of the star constellations so defining time with base 10 would be difficult. In many cultures around the world, there are 12 months in a year and are often represented with creatures real or mystical (like the Chinese and Greek zodiacs),  Time within the day is measured using hours, minutes, and seconds. There are 60 seconds in a minute and 60 minutes in an hour. There are two 12 hour half days in a day. For time, sometimes in English 7:15 will be stated as a quarter past 7, since 15 is a quarter of 60. 7:30 will be stated sometimes as half past 7, since 30 is a half of 60. 

After doing some research, I’ve found out that there are more uses for 60 in the [Babylonian] numeration system. For example the harmonic connotations. The number 60, being a multiple of 12, might have cultural or religious connotations in societies that revered the number 12. The Babylonians used base 60 for their calculations, and many of their mathematical/astronomical findings were foundational for subsequent civilizations, which lead to 60 being used instead of 10. The number 60 is also the lowest common multiple of all the numbers 1 through 6. This makes it easy to integrate or switch between different bases, such as base 2, 3, 4, 5, 6 within a base 60 framework. This property cannot be offered with base 10.