# Why is a circle 360 degree?

1. Aug 25, 2009

### crays

Hi, i'm just wondering why is a circle 360 degree? Why not put it 400 for easy calculation?

2. Aug 25, 2009

### junglebeast

"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."

Basically, If I understood that correctly, a hexagon (having 6 sides) is similar to a circle, and if you choose a hexagon with a radius of 1 unit then the perimeter is 6 units, but in their number system 1 unit is 60 of our units, so they chose the number of degrees in a circle to be the same as the perimeter of a "unit-hexagon", or 360.

3. Aug 25, 2009

### mgb_phys

It's easy to divide by lots of other numbers, especially if you also use 12.
It's all the fault of those crazy Babylonians - the same reason we have 60 secons and 60 minutes

ps. You can divide a circle into 400, it's called 'gons' but apart from a few French surveyors nobody uses it - it just annoys software developers.

4. Aug 25, 2009

### Elucidus

This has to do with the cultures that developed the concept of "degrees." (Note it is a purely artificial measure.) The cultures (Babylonian, Sumerian, etc.) that developed angle measures many centuries ago used sexigesimal numeration (base-60) and were particularly fond of equilateral triangles. It appears that the base angle of such a triangle was ascribed a "perfect" measure of 1 unit, broken into 60 parts (or degrees). Since 6 such angles arranged around a point forms a full revolution, we get the 360 degrees familiar today.

Or ar least that is the current best thinking on the matter that I am aware of.

--Elucidus

5. Aug 25, 2009

### crays

Thanks for the info. lol, i didn't know they existed XD. I mean the 'gons' thing. The babylonians count in base of 60, meant that they go from their 1 to 60 before going to our 10?

6. Aug 25, 2009

### mgb_phys

A bit of both, they had symbols for 1 and 10 (like the romans) but use them to count up to 60 then went to the next column ( 60 is handy for doing division because it divides by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30) so a hundred would be 1 '60' and 4 '10's

The gon is one of the french revolution attempts to make sensible metric measurements - but never really caught on. Like metric time (100 secs in a minute and 100 mins in an hour) it doesn't really have any advantages over splitting an angle into 90deg.
Another useful angle unit that never caught on outside the rather specialized business of dropping shells on people is the artillery mil. Divide a circle into 6400 (roughly 2pi*1000) and an angle of 1mil means 1m at 1000m (or 1ft at 1000ft).

Whats more remarkable is that using 60 survived unchanged from the first written culture to still annoying programmers today who have to deal with units of 123O 45' 67" in GPS

Last edited: Aug 25, 2009
7. Aug 25, 2009

### skeptic2

I heard that it was because a year was thought to have 360 days and the sun moved 1 degree per day along the ecliptic.

8. Aug 25, 2009

### g_edgar

Back in 1789 when the French promulgated the metric system, they did propose to divide the circle into 400 grads. Maybe your calculator even has that mode. But I have never had occasion to use it. It was about as successful as their 10-day-a-week, 3-week-a month calendar!

9. Aug 26, 2009

### HallsofIvy

Staff Emeritus
And, of course, the really useful measure is "radians"- with $2\pi$ radians to a circle!

10. Aug 26, 2009

### Preno

How would that result in easier calculation? 400 is not even divisible by 3.

11. Aug 26, 2009

### mgb_phys

It does in navigation, a 16 point compass rose (ENE etc) divide conveniently into 400 but not 360

12. Aug 26, 2009

### skeptic2

There is an old anecdote about a math teacher with a smart kid in the class.

Teacher: Okay Johnny, how many of the numbers from one to ten are evenly divisible by 2?
Johnny: All of them.
Teacher: How would you divide 5 evenly by 2?
Johnny: 2 1/2 and 2 1/2.

13. Aug 26, 2009

### DaveC426913

12 would have been a much better numbering system than 10.
10 is only divisible by 1, 2 and 5. You can't even divide it into quarters or thirds.

12 is divisible by 1,2,3,4 and 6.

You can see why the Sumerians chose 60; it is divisible by the first six numbers.

14. Aug 27, 2009

### nirax

the only hitch is that the damn monkeys from which we evolved got only 10 fingers ... so the ancients which were closer to monkeys than us and didn't have the (dis)advantage of MS Excell wouldn't know how to count till 12 with only 10 fingers ...

we still do not know but we can confuse ourself with more sophisticated things so we dont care.

15. Aug 27, 2009

### mgb_phys

It's easier to count to 12 on your fingers than 10 !
Moving your thumb over the tip and each joint on one hand is a lot quicker than folding fingers in (especially the ring finger) on both hands. And has the advantage that you can do it while holding a gate open or a shepherd's stick with the other hand.

There used to be a theory that people counted to 8 using the thumbs and finger tips - that's why the word for 9 is similar to 'new' in a lot of languages - it was a new number. But sheep counting rhymes that predate the celts seem to be base 5 and 10 so it's been disgarded.

16. Aug 27, 2009

### g_edgar

Aha! Some obscure country STILL maintains that a yard subdivided into 36 inches is far superior to a meter subdivided into 100 centimeters...

17. Aug 27, 2009

### DaveC426913

Who uses yards as a measurement of anything? :uhh:

18. Aug 29, 2009

### Staff: Mentor

American football for one.

A significant deterrent for the US to wholeheartedly adopt the metric system is property descriptions, all of which are measured in feet. If we in the US were to discard the English system, every piece of property would have to be resurveyed, or at least, would need its description converted to metric measurements.

Here is a portion of the description of some property I own (underlines added by me):

"The North 555.10 feet of the East half of the Northwest quarter of the Northeast quarter of Section 21, Township 30 N. Range 6 West, W.M., EXCEPT that portion of the above described property lying easterly of the following described "Line 1":
"Line 1"
Beginning at a point lying North 89°54'22" West, a distance of 109.20 feet from the Northeast quarter of said Section 21; thence South 1°45'18" West to a point lying 555.10 feet South, as measured at right angles from the North line of said Section 21 and the end of "Line 1". "

The description goes on with about a half-page of exceptions.

In addition to the obvious measurements in feet, descriptions also situate the property in a given section, which is a square mile or 640 acres.

It would be a daunting task to convert all of these property descriptions.

19. Aug 29, 2009

### DaveC426913

It would be a daunting task to fly a probe to Mars too. After a few crashes, I wonder of converting to the same system as the rest of the world might look more appealing.

20. Aug 29, 2009

### aPhilosopher

I've gotta toss in in favor of the radian as well. It has the advantage that to figure out the arc-length of a circle subtended by an angle, one just multiplies the radius by the angle! It's even linear in the radius. Very nice. And all the formulas come out nicer as well. I honestly think in radians and have to think for a second when people throw degrees at me.