Why 360-degrees?

[Robust]

Why not, say, 400-degrees to describe circumference of the circle?

[User2983]

i actually think i know this one. I'm pretty sure the number came back from Sumerian time where they used the sexagesimal(60-based) couting system. It's appealing because so many integers divide evenly into it. 360 is a multiple of 60 and a lot of integers divide evenly into it also. That's what I heard before and I'm pretty sure it's right. ;)

[C1ay]

Why not, say, 400-degrees to describe circumference of the circle?

Because that would be gradians, not degrees.

[Turtle]

___I do not follow C1ay; it is after all an arbitray division. 360 is curiously close to the number of days in a year I note.

___The idea of the easy divisability is not without merit however, & may have some influence. I don't recall the Sumerians having zero either, which strictly is required to use a 'base' system of any kind.

___Good question though which we should persue a bit more I imagine.

[C1ay]

___I do not follow C1ay; it is after all an arbitray division. 360 is curiously close to the number of days in a year I note.

___The idea of the easy divisability is not without merit however, & may have some influence. I don't recall the Sumerians having zero either, which strictly is required to use a 'base' system of any kind.

___Good question though which we should persue a bit more I imagine.

In ancient times the year was divided into 360 days. My remark to robust though has to do with a system of angular measure that divides a circle into 400 parts instead of 360. The word 'gradians' in my previous post is a link to MathWorld on this.

[Turtle]

___C1ay said. "In ancient times the year was divided into 360 days."

___If Earth's rotation is slowing as discussed in another thread, how far back in history must we go to find a faster spin which would result in a 360 day year? I know extra days were added to compensate the calendar in recorded history, but I mean much further back. Something to think about anyway. ;)

[Queso]

like millions of years

[Buffy]

how far back in history must we go to find a faster spin which would result in a 360 day year? I know extra days were added to compensate the calendar in recorded history, but I mean much further back. Something to think about anyway. ;)

Turtle! I'm surprised! 2milliseconds per hundred years! Do the math! ;)

 

Computationally,

Buffy

[C1ay]

___C1ay said. "In ancient times the year was divided into 360 days."

___If Earth's rotation is slowing as discussed in another thread, how far back in history must we go to find a faster spin which would result in a 360 day year? I know extra days were added to compensate the calendar in recorded history, but I mean much further back. Something to think about anyway. ;)

That's backwards isn't it. At 365 days per year we are making 5 revolutions more per year than the past meaning the Earth sped up at some point or time keeping was off by that much in the past, timekeeping has my vote. I have heard christians posit that this was caused by the flood resulting from the 40 days and nights of rain.

[Turtle]

___I don't think it was backwards. Let's see; if the time Earth takes to orbit the Sun doesn't change (ie the length of a year), then we say the Earth revolution is 1. Now to the number of rotations on its axis Earth makes, it is some number over 1 revolution. Now if the rotational speed increases, then the number of those rotations in the year decreases.

___This brings us back to the point of how fast of an Earth spin gives 360 rotations in a revolution around the Sun. (Forgive me not doing the math Buff, beleive it or not the specifics confuse me while the generality seems obvious)

___As to the changing of Earths rotational speed, I posit it is not some smooth curve in one direction. As we saw with the Sumatra quake/tsunami, singular events can have immediate effects. As I pointed out in another thread, a large aseroid impact will either slow us or speed us depending on which direction/vector it takes to impact.

___We still can ask if the 360 day year dates back to some ancient time when the Earth year was 360 days.

[C1ay]

___I don't think it was backwards. Let's see; if the time Earth takes to orbit the Sun doesn't change (ie the length of a year), then we say the Earth revolution is 1. Now to the number of rotations on its axis Earth makes, it is some number over 1 revolution. Now if the rotational speed increases, then the number of those rotations in the year decreases.

___This brings us back to the point of how fast of an Earth spin gives 360 rotations in a revolution around the Sun. (Forgive me not doing the math Buff, beleive it or not the specifics confuse me while the generality seems obvious)

___As to the changing of Earths rotational speed, I posit it is not some smooth curve in one direction. As we saw with the Sumatra quake/tsunami, singular events can have immediate effects. As I pointed out in another thread, a large aseroid impact will either slow us or speed us depending on which direction/vector it takes to impact.

___We still can ask if the 360 day year dates back to some ancient time when the Earth year was 360 days.

While it's possible, I don't think the time to orbit the sun changed, just the number of Earth revolutions per orbit.

 

I think the actual reason for a 360 day year in the past was the ease of rounding everything to twelve 30 day months. As man's math got better so did his time keeping.

[Turtle]

___While waiting for a math answer, I beg to differ once again. Our current calendar is in no way logical in an efficiency sense; make that calendars, because may cultures & sciences do not reference the Gregorian calendar.

___I specifically stated that the Earth's revolution remained static so as not to invoke that discussion of its potential change in the rotation aspect. It seems likely revolution velocity too has changed over time for the same reasons given for Earth's slowing, ie tidal forces, & including asteroid impacts.

___More to the point of the thread, regardless of the Earth rotation, it is facility of math I believe 360 is used. The circle afterall relates to considerable more human concerns & endeavors than the home planet's rotation.

[C1ay]

More to the point of the thread, regardless of the Earth rotation, it is facility of math I believe 360 is used. The circle afterall relates to considerable more human concerns & endeavors than the home planet's rotation.

That's what I was trying to imply with ease of rounding.

[Robust]

i actually think i know this one. I'm pretty sure the number came back from Sumerian time where they used the sexagesimal(60-based) couting system. It's appeling because so many integers divide evenly into it. 360 is a multiple of 60 and a lot of integers divide evenly into it also. That's what I heard before and I'm pretty sure it's right. :Alien:

My research shows it to be of Babylonian extraction, which predates the Sumerian, and most particularly because 360 degrees coincides with the Base 10 number system, which also is Babylonian and of which school Pythagoras was a student (and perhaps teacher).

 

It is speculation on my part,but I have to think that the perfect ratios given by Pythagoras derive from is Babylonian tenure and as expressed in every regard as confirming both the Base 10 number system and 360-degree circle. Probably the most convincing evidence showing this relationship is the given formula of pi/40, where 40 is given as representing the circle's 4 quadrants relevant to Base 10 (which Pythagoras undoubtedly refers to as the cipher), thus the formula of pi/40 as giving the distance between each adjacent angular degree of the 360-degree circle; or as I believe Pythagoras may have looked upon it from the standpoint of the cipher representing 10, and considering the 4 quadrants of the circle: 40 (9) = 360 degrees.

 

The interpretation may be lacking, but the figures do add up.

[Damo2600]

Interesting so pi/10 would give you the first 90 degree quadrant and pi/(1/9) would give you a degree. Right?

 

I think C1ay is right. It also must have something to do with the radius. Otherwise if the degrees were 400 the expression:

 

degree distance = radius/radians,

 

as Robust pointed out, would not give an actual degree.

 

Just a clue to your problem.

 

Damien

[Robust]

___While waiting for a math answer, I beg to differ once again. Our current calendar is in no way logical in an efficiency sense; make that calendars, because may cultures & sciences do not reference the Gregorian calendar.

___I specifically stated that the Earth's revolution remained static so as not to invoke that discussion of its potential change in the rotation aspect. It seems likely revolution velocity too has changed over time for the same reasons given for Earth's slowing, ie tidal forces, & including asteroid impacts.

___More to the point of the thread, regardless of the Earth rotation, it is facility of math I believe 360 is used. The circle afterall relates to considerable more human concerns & endeavors than the home planet's rotation.

Well put, Turtle....and more to the point.

[Robust]

Interesting so pi/10 would give you the first 90 degree quadrant and pi/(1/9) would give you a degree. Right?

 

I think C1ay is right. It also must have something to do with the radius. Otherwise if the degrees were 400 the expression:

 

degree distance = radius/radians,

 

as Robust pointed out, would not give an actual degree.

 

Just a clue to your problem.

 

Damien

Yes it does, Damien. radius/radian gives the degree-distance precisely, as can be shown conversely by pi/40 - or as shown more elaborately in my Base 10 Anomaly post. All by reason that the radian is the same distance on the arc as that of the radius subtending it.