# Naked Science Forum

## General Science => General Science => Topic started by: chris on 10/08/2012 09:31:09

Title: Why are there 360 degrees in a circle?
Post by: chris on 10/08/2012 09:31:09
Why are there 360 degrees in a circle? What was the basis of that and how did it come about?
Title: Re: Why are there 360 degrees in a circle?
Post by: CliffordK on 10/08/2012 10:00:51
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.
Title: Re: Why are there 360 degrees in a circle?
Post by: William McCormick on 10/08/2012 13:34:09
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
Title: Re: Why are there 360 degrees in a circle?
Post by: Boogie on 10/08/2012 19:23:25
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."
Title: Re: Why are there 360 degrees in a circle?
Post by: Geezer on 10/08/2012 20:06:01
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.
Title: Re: Why are there 360 degrees in a circle?
Post by: Bored chemist on 11/08/2012 12:56:07
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.
Title: Re: Why are there 360 degrees in a circle?
Post by: CZARCAR on 12/08/2012 16:47:28
12 months/yr X 30 days/month = 360?
Title: Re: Why are there 360 degrees in a circle?
Post by: William McCormick on 12/08/2012 18:47:25
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
Title: Re: Why are there 360 degrees in a circle?
Post by: Bored chemist on 12/08/2012 20:48:38
Here's a picture for you
http://www.fig.net/pub/cairo/papers/wshs_01/wshs01_02_wallis.pdf
Title: Re: Why are there 360 degrees in a circle?
Post by: Don_1 on 25/08/2012 02:09:51
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.
Title: Re: Why are there 360 degrees in a circle?
Post by: imatfaal on 26/08/2012 23:21:57
mod note

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