[chris (OP)]

Why are there 360 degrees in a circle? What was the basis of that and how did it come about?

[CliffordK]

You could also say that there are  6.2831853072 radians in a circle.

I'm seeing notes that degrees in a circle is a concept that would be thousands of years old, and may be based on a 360 day year. 
http://www.wonderquest.com/circle.htm
http://en.wikipedia.org/wiki/Degree_%28angle%29#History

A 30 day month, 360 day year would be convenient, but it would drift quickly.  In a decade it would be off by 52 days.

It is also noted that 360 can be divided by 2, 3, 4, 5, 6, 8, 9, and 10 (skipping 7), which would make it excellent for designing geometric shapes.  Perhaps also good for designing many gears.

[William McCormick]

You are correct about 360 being a flexible number. 360 degrees can also be divided by 24 as in hours it takes the earth to complete one revolution.

It also works well with 60, 3600 and 86,400 the number of seconds in one revolution of the earth.


             Sincerely,


                      William McCormick

[Boogie]

From "A History of Pi" by Petr Beckmann, a mathematician from Czechoslovakia.

  "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."

[Geezer]

It's really pretty obvious.

The ancients understood that the circumference of a circle is three times its diameter (realize that they only had bits of string to make the measurements, so they were not that far off.) They were really more concerned with dividing up right angles (North versus West etc) so, understanding the importance of the three thing, they chopped the right angle into three bits, then chopped each of those into three bits. As they had ten fingers, they divided each of the smaller divisions into ten bits.

3x3x10=90

The rest is history.

[Bored chemist]

It's really pretty obvious.

The ancients understood that the circumference of a circle is three times its diameter (realize that they only had bits of string to make the measurements, so they were not that far off.)

The ancients who defined the degree knew perfectly well that pi wasn't 3 so that "explanation" doesn't make sense.

[CZARCAR]

12 months/yr X 30 days/month = 360?

[William McCormick]

From "A History of Pi" by Petr Beckmann, a mathematician from Czechoslovakia.

  "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."

I would have liked to have seen the original notation.

                      Sincerely,

                            William McCormick

[Bored chemist]

Here's a picture for you
http://www.fig.net/pub/cairo/papers/wshs_01/wshs01_02_wallis.pdf

[Don_1]

I thought it was down to the ancient Egyptians. They divided the year into 360 days. They knew that this was wrong, but it fitted their liking for nice even numbers. The remaining 5 days were deemed to be for the gods.

[imatfaal]

mod note

I split off William's notions about ratios.  Please keep to the OP