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What's the reason we agreed to setting the number of degrees of a full circle to 360? Does that make any more sense than 100, 1000 or any other number? Is there any logic involved in that particular number?

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    $\begingroup$ Speculation about why the degree was chosen as it was can be found here. $\endgroup$ Mar 25 '13 at 8:54
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    $\begingroup$ I think you can probably blame the Babylonians, who loved to count in base 60, but this should probably be moved to the maths site. You're more likely to find a math history expert there. :) $\endgroup$
    – Michael Brown
    Mar 25 '13 at 8:54
  • $\begingroup$ Possible duplicate: math.stackexchange.com/q/142735/11127 $\endgroup$
    – Qmechanic
    Mar 25 '13 at 9:16
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As it has been replied here - on Wonder Quest (webarchive link):

The Sumerians watched the Sun, Moon, and the five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn), primarily for omens. They did not try to understand the motions physically. They did, however, notice the circular track of the Sun's annual path across the sky and knew that it took about 360 days to complete one year's circuit. Consequently, they divided the circular path into 360 degrees to track each day's passage of the Sun's whole journey. This probably happened about 2400 BC.

That's how we got a 360 degree circle. Around 1500 BC, Egyptians divided the day into 24 hours, though the hours varied with the seasons originally. Greek astronomers made the hours equal. About 300 to 100 BC, the Babylonians subdivided the hour into base-60 fractions: 60 minutes in an hour and 60 seconds in a minute. The base 60 of their number system lives on in our time and angle divisions.

An 100-degree circle makes sense for base 10 people like ourselves. But the base-60 Babylonians came up with 360 degrees and we cling to their ways-4,400 years later.

Then, there's also this discussion on Math Forum:

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 $ \frac{57}{60} + \frac{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 ... $\pi = \frac{25}{8} = 3.125$.

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  • $\begingroup$ While it seems likely that 360 is related to the number of days, I would like to know what exactly would be meant by "the circular track of the Sun's annual path across the sky". $\endgroup$ Aug 9 '17 at 13:50
  • $\begingroup$ @MarekFekete perhaps they are referring to the ecliptic motion of the sun? $\endgroup$ Oct 4 '20 at 9:32

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