# Why 360 deg.

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The question is simple why is it 360 deg in a circle and not a number that is easier to work with. More importantly were does the number "360" come from when was it chosen why was it chosen and by who?

P.S. What other units of mesurement are used to mesure angle?

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Why isn't 360 easy to work with? It is divisible by 2,3,4,5,6,8,9,10,12,15,20,30,45, etc.

In short it is a very useful base, that probably comes from older civilizations use of base 60.

Radians are also used, and preferred in all but baby uses of geometry (ie high school) since they have much nice analytic properties - it is the natural unit for physics eg in measuring angular momentum, and is the natural unit for sin and cosine, for then differentiating sin gives cos and differentiating cos gives -sin: using degrees yields multiplicative constants to deal with. This is analogous to the fact that natural logs and base e are indeed natural.

If you dislike 360, then you onw't like radians since there are 2pi radians in a circle.

Some places also use gradians: there are 400 gradians in a circle.

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One of the ancient civilisations - I think the Babylonians - believed that there were 360 days in a year, and thus it would be logical for a circle to have 360 degrees.

I'm not sure if they were heliocentric though.

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the french cam up with the grad, which is 400 instead of 360.

personally, i like radians. they are easy to work with and aren't random. $C=2\pi{r}$ let r be one unit. that makes $C=2\pi$. one revolution is $2\pi$, half a revolution is $\pi$, quarter revolution is $\frac{\pi}{2}$ and so on.

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I had this discussion with my old maths teacher quite a few years back. I believe the primary reason for choosing 360 as the number of degrees was as matt said - lots and lots of numbers divide it, making life a little easier when you're working with geometric shapes.

The French did indeed create the grad unit of measurement. At the time of the French revolution, they tried to metricise everything - including time. Hence, 100 grads in a right angle. Unfortunately, it didn't really seem to catch on (except in some areas of engineering, I believe).

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It is purely sepculative, obviously, but it does seem a more than reasonable explanation. Ok, perhaps no one sat down and said: right let's pick a base with lots of divisors, but it evolved in such a way. Another example, and one perhaps more readily agreeable, is the old predecimal currency in the UK. There used to be 240 pennies in the pound, making it very useful for trading in commoditities since it is readily divisible by 2,3,4,5,6,8,10, etc. In fact the most annoying thing is that it isn't divisible by seven, and there are seven days of the week. A fact that is enshrined in the old unit of a Guinea, which was 245 pence (1 pound and one shilling), which is divisible by 7, and which is still the unit in which horses are priced.

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360 is a "highly divisible number" - that is, it is the first number with at least as many factors as it has. 360 has 24 factors - 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

-Uncool-

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the first number with at least as many factors as it has.

Huh?

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One of the ancient civilisations - I think the Babylonians - believed that there were 360 days in a year' date='[/b'] and thus it would be logical for a circle to have 360 degrees.

I'm not sure if they were heliocentric though.

We are very fortunate that they didn't know there were 365.2 then!

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We are very fortunate that they didn't know there were 365.2 then!

Or that they didn't measure the year in radians

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Edward, 360 is the first number with 24 factors - that's what I'm saying.

-Uncool-

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Ok now what is special about 24?

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It is purely sepculative, obviously, but it does seem a more than reasonable explanation. Ok, perhaps no one sat down and said: right let's pick a base with lots of divisors, but it evolved in such a way. Another example, and one perhaps more readily agreeable, is the old predecimal currency in the UK. There used to be 240 pennies in the pound, making it very useful for trading in commoditities since it is readily divisible by 2,3,4,5,6,8,10, etc. In fact the most annoying thing is that it isn't divisible by seven, and there are seven days of the week. A fact that is enshrined in the old unit of a Guinea, which was 245 pence (1 pound and one shilling), which is divisible by 7, and which is still the unit in which horses are priced.

That's why there are Guineas and Pounds?

So, is a Guinea still 245 pence, or did that change with decimalization?

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im pretty sure that the reason is that the ancient sumerian civilation counting system had a base 6 system so the number would be equivilant to the number 1000 in our base 10 system.

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A guinea is still one pound one shilling, or 1 and 1 twentieth of a pound, or £1.05 in new money, I imagine.

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Just that it makes the 360 neither too high, nor too low, Edward.

-Uncool-

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Ok but what is the thing with 24??? And what exactly did your sentence I quoted mean?

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Y'know, my main problem with 360 degrees in a circle is that there are 360 degrees in a square. If you move on from a square to a pentagon, you get 540 degrees. As you move up closer and closer to the infinite amount of "sides" that a square has, shouldn't you end with infinite degrees?

But I also understand how you can make 360 degrees work by counting the degrees in the center (which is what we do) rather than the outside "corners" between the infinitesimal sides.

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What was the most important thing to early civilisations?

Wheat crops.

What did they need to know above all else.

Planting and harvest time.

What big white thing in the sky told them that?

and the complexity of civilisation makes you break 12 down into finer and finer divisions.

360 degrees.

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• 5 weeks later...

I should learn to stay out of threads like this because, simply, I just don't have the math skills for it. Anyhoo....I believe the reason for 360-degrees is simply because the earth revolves on its axis relative to the sun at the rate of 1-degree every 15 minutes Thus in a 24-hour period of time: 15*24 = 360.

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It was influenced by the Babylonians, they used 60 as their base number, that is the reason we have 60 seconds, 60 minutes, and they also like 360 because it was roughly the time of a year but they rounded to that to keep in sync with their number system well. I believe it is a terrible unit for dividing a circle regardless of how less it creates fractions. One revolution should equal 1 degree should equal 1 centi-degree.

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• 2 weeks later...
I should learn to stay out of threads like this because, simply, I just don't have the math skills for it. Anyhoo....I believe the reason for 360-degrees is simply because the earth revolves on its axis relative to the sun at the rate of 1-degree every 15 minutes Thus in a 24-hour period of time: 15*24 = 360.
This argument is backwards. It is because there are 360 degrees in a complete revolution that each degree takes 15 minutes to traverse.

There really is no further need for "here's what I think is the reason..." posts. Matt, Lyssia and Dave have essentially revealed the likely historical reasons for the choice :

(i) 360 is very divisible;

(ii) The Sumerians worked with base 60 and the Egyptians sometimes used base 12. One or the other of these folks likely came up with the 360 degree angle for a complete revolution;

(iii) The solar year may have thought to have had 360 days.

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Is there a number below 360 that has more positive divisors than the number of positive divisors for 360?

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BigMoosie is correct. It all started with the Babylonians.

While their maths was in base 10, their accounting was in base 60. Since 60 baskets of grain are a lot easier to divide in many different ways than 100 baskets. This practice followed on into measurement. A Circle with 60 degrees would be too cumbersome, so they used 6x 60 degrees and got 360 degrees. Quite a simple and elegant solution I thought.

A surprising number of things we take for granted go back a long way.

Why is "clockwise" clockwise?

Why is the standard wheel track of a car 4' 8"?

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