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whozum

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- Thread starter whozum
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In summary, the number 360 was chosen to be the number of degrees in a complete revolution because of its divisibility and connection to the number of days in a year. This number was first used by the Babylonians, who inherited it from the Sumerians. The Babylonians used a sexagesimal system, with a base of 60, which allowed for easier calculations and avoidance of decimals. The reason for this specific base is unknown, with many theories but no conclusive answer. Alternatives such as a base of 120 would have made calculations more difficult.

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whozum

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Mathematics news on Phys.org

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gregmead

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I'm not too good on the history of science...

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whozum

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There are easier numbers to divide. I just don't see any logical sense as to why 360 was chosen.

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gregmead

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I still think its something to do with the number of days in the year...

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Huckleberry

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In 1936, a tablet was excavated some 200 miles from Babylon. Here one

should make the interjection that the Sumerians were first to make one of

man's greatest inventions, namely, writing; through written communication,

knowledge could be passed from one person to others, and from one

generation to the next and future ones. They impressed their cuneiform

(wedge-shaped) script on soft clay tablets with a stylus, and the tablets

were then hardened in the sun. The mentioned tablet, whose translation

was partially published only in 1950, is devoted to various geometrical

figures, and states that the ratio of the perimeter of a regular hexagon

to the circumference of the circumscribed circle equals a number which in

modern notation is given by 57/60 + 36/(60^2) (the Babylonians used the

sexagesimal system, i.e., their base was 60 rather than 10).

The Babylonians knew, of course, that the perimeter of a hexagon is

exactly equal to six times the radius of the circumscribed circle, in fact

that was evidently the reason why they chose to divide the circle into 360

degrees (and we are still burdened with that figure to this day). The

tablet, therefore, gives ... Pi = 25/8 = 3.125.

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gregmead

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cool :D - well at least I learned something new staying up this late revising...

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whozum

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Huckleberry

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It was during the reign of Nebuchadnezzar (605-562 BC) in the Chaldean dynasty in Babylon that the circle was divided into 360 degrees. This was because the Chaldeans had calculated by observation and inference that a complete year numbered 360 days. The basis of angular measure for the mathematicians of Babylon was the angle at each of the corners of an equilateral triangle. They did not have decimal fractions and thus found it difficult to deal with remainders when doing division. So they agreed to divide the corner of an equilateral triangle into 60 degrees, because 60 could be divided by 2, 3, 4, 5 and 6 without remainder. Each degree was divided into 60 minutes and each minute into 60 seconds. If the angles at the corners of six equilateral triangles are placed together they form the angle formed by a complete circle. It is for this reason that there are six times 60 degrees of arc in the complete circle.

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whozum

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Interesting stuff, thanks alot.

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Night Owl

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Huckleberry

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59 actually. no zeros at that time I think.

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html

Looking at this it appears they almost did use a base 10. For some reason they decided not to stop at 10 and went all the way to 60, repeating the series all the way. Hmm, would this also be because more numbers are divisible into 60 than 10?

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html

Looking at this it appears they almost did use a base 10. For some reason they decided not to stop at 10 and went all the way to 60, repeating the series all the way. Hmm, would this also be because more numbers are divisible into 60 than 10?

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whozum

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Huckleberry

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This comes from the site posted above. They go over some possible explanations, but none are conclusive. There may not be an answer.Finally we should look at the question of why the Babylonians had a number system with a base of 60. The easy answer is that they inherited the base of 60 from the Sumerians but that is no answer at all. It only leads us to ask why the Sumerians used base 60. The first comment would be that we do not have to go back further for we can be fairly certain that the sexagesimal system originated with the Sumerians. The second point to make is that modern mathematicians were not the first to ask such questions. Theon of Alexandria tried to answer this question in the fourth century AD and many historians of mathematics have offered an opinion since then without any coming up with a really convincing answer.

Looking at their system of numerals it looks like using a base of 120 would give them one more numeral that would not result in decimals and would create much more difficulty in expressing those numbers. The example in the text states that 424000 would be written in Sumerian by using the numbers 1,57,46,40. They would have to calculate 1 x 60^3 + 57 x 60^2 + 46 x 60 + 40 = 424000. With a base of 120 they would need over twice as many numerals and would need to calculate by hand much larger numbers. That is my guess.

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whozum

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Huckleberry

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Very true. Your guess is as good as mine, probably better. My understanding of math sucks.

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whozum

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Thanks for the help man.

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uart

Science Advisor

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whozum said:

This is just a total guess, but I imagine the reason for using such a large base might have been because they (or those from whom they inherited the system) started out without only single symbol representations for all the numbers considered important to them. It's possible that when they started out that no one could imagine a use for a number greater than 60. Perhaps only later someone thought up the "juxiposition" notation for numbers greater than 60 and by then they needed to keep the same sixty digits for "backward compatibilty".

360 degrees in a revolution is significant because it represents a full circle or a complete rotation. It has been used as a unit of measurement for angles and rotations for centuries.

The concept of 360 degrees in a revolution is believed to have originated from ancient civilizations such as the Babylonians and Egyptians who used a sexagesimal system for counting and measuring. This system was based on the number 60, which is divisible by many numbers including 360, making it a convenient choice for measuring angles and rotations.

360 degrees in a revolution is used in navigation and astronomy because it allows for precise measurements and calculations. It is also a universal unit of measurement that is recognized and used by people all over the world.

Yes, it is possible to have more or less than 360 degrees in a revolution. For example, a full circle in a polar coordinate system is represented by 2π radians, which is approximately equivalent to 360. However, in some cultures, such as the ancient Mayans, a different system of measurement was used where a full circle was divided into 400 degrees.

The concept of 360 degrees in a revolution has evolved over time with the development of more accurate and precise measurement tools. In addition, different cultures and societies have developed their own systems of measurement, leading to variations in the use of 360 degrees in a revolution.

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