Degrees of a Circle: How Much & Why 360

[physicsuser]

IHow much is a degree and why there are 360 of the in a circle?

 

[jcsd]

a dgeree is 60 'arc minutes' or 3600 'arc seconds' or pi/180 radians or 10/9 of a gradian or 1/360th of a full rotation.

The reason there are 360 of them in a circl;e is that the ancient Sumerians were very found of base-60 number systems (as 60 is the lowestn number to be exactly divisble by the first six numbers).

 

[mathwonk]

you answered your own question, physics user, when you said there are 360 degrees in a circle. I.e. a degree is one part of a circle when the circle has been divided into 360 equal parts. so what was your question really? this is why the previous responder does not quite know how to respond and is trying everything possible.

 

[BobG]

A circle is broken into 360 degrees because the Babylonians and Sumerians were measuring how much a star moves in the sky relative to the day before. In other words, one degree is the relative change of position from one day to the next (approximately).

Obviously we see the stars moving across the sky over the course of the night, but at 12:00 midnight, say, a star would be located at a given point in the sky. The next night, at 12:00 midnight, the star would have shifted a little in the sky - by almost one degree. In fact, over the course of a year, the star will shift 360 degrees, returning almost exactly to it's location at midnight one year earlier.

All are approximate, since you could not measure star locations precisely unless you could also measure time precisely, and 360 is a much easier number to work with than 365 if you're building your whole numbering system on the tracking of the stars.

A base-60 numbering system reflected the fact that the Babylonians and Sumerians were among the first to use the stars for navigation. The practical use of navigation by the stars drove the invention of their numbering system.

In other words, is was the approximately 360 days in a year that drove the base-60 numbering system vs. the other way around.

The Sumerians invented this system, but the Babylonians are more well known for it, since it was they who passed this on to the Arab world to be spread to other civilizations.