Making 360 Days in a Year

Ancient Maya around a thousand years ago, and independently ancient Babylonians, over three thousand years ago, counted the days in the year and as a first approximation arrived at 365 days per year. In each case people were counting at about the same time that their culture was developing a numbering system and struggling with how to deal with addition, subtraction, multiplication and division. Three hundred and sixty five is not a very friendly number to people who are only beginning to understand arithmetic. For example it is only divisible evenly by 5 and 73. It is also a large number and large numbers are most easily dealt with if they can be though of as groupings of smaller numbers. For example in our modern base ten counting system 365 is reckoned as three groups of one hundred items plus six groups of ten items plus five items--a rather complicated assemblage of groupings that must to be added together, but still much simpler than dealing with 365 individual items.

We might also think of 365 as 73 groups of 5 items each. But 73 is still a large number of groups to have to deal with. Alternatively we might thing of 365 as 5 groups of 73, but 73 is a large number of items keep track of in a single group. It would be much easier if one could deal with 360 days in a year. That could be thought of as 12 groups of 30 days each. And in fact that is what the ancient ancient Babylonians did. In order to be able to deal with 360 days in a year rather than the more difficult number of 365 days they decided to count the first 360 days in the year. The ancient Maya had the same problem with 365 days and solved it in nearly the same say. The Maya only counted the first 360 days in the solar year and treated it as 18 groups (or months) of 20 days each. Each culture then added 5 days on at the end of the 360 day year. They were special days and for the ancient Egyptians they became holidays. (Today we still are on the outlook for a good reason to have another holiday.) The Maya added a short 5 day "month" to the 18 other 20 day months. Problem solved.

Babylonian arithematic on a clay tablet (Plimpton

322); photo by the British Museum.

Interestingly theBabylonians adopted a numbering system which seems to be tailored to deal with 360. Apparently this occurred because 360 is easily divisible by a number of factors without the need for elaborate fractions or decimal notation. For example one half of 360 is 180, an integer. One third is 120, an integer. One fourth is 90, a fifth is 72, a sixth is 60, a seventh is not an integer, an eigth is 45, a ninth is 40, a tenth is 36, an eleventh is not an integer, a twelfth is 30, a fifteenth is 24, etc. Probably because 360 is six times sixty the Babylonians found it convenient to express numbers in a base sixty system. They also expressed all fractions as multiples of 1/60. Thus one half is 30 sixtieths, one third is 20 sixtieths, one fourth is 15 sixtieths etc. The Maya developed a numbering system based on groupings of 20. The 360 days in a "year" were easily expressed as 18 groups of 20, the basis of one of their calendars, the Haab calendar.

Our measuring 360 degrees in a circle today is a vestige of the counting of 360 days in a year several thousand years ago. Small angles are measured in one sixtieth of a degree or an arc minute today because Babylonians developed a fraction system based on a sixtieth of a degree several thousand years ago. They also divided the day and night into 24 hours, each hour into 60 minutes, and each minute into 60 seconds--a perfectly natural thing to do when dealing with a base 60 numbering system. Thus today we still designate the time of day using the Babylonian divisions.

If you would like to learn more about all kinds of calendars consult the excellent site Calendar Zone! There you will find descriptions, links and even software to convert from one calendar system to another.

This page prepared by C.Hartley, Director of the Ernest B. Wright Observatory at the Department of Physics at Hartwick College in the City of Oneonta, NY. More things from C. Hartley at his home.