Why are there 360 degrees in a circle and not 1,000?
The Sunday Nation
Nairobi,
27 October 2013
After reading the explanation of the origin of the value of the mathematical number pi, Joseph Mwangi wrote: “I have learned more from your column than from school. No teacher ever explained to me where pi comes from, but now I know. Would you also explain why a circle has 360 degrees? Why not a nice round number like 100 or 1,000?”
Well Joseph, the truth is that a circle can have as many degrees as you like. The reason being that degrees are an arbitrary quantity chosen to suit the particular situation one is concerned with…and they are not restricted to angles only.
Degrees are also found in temperature – water boils at 100 degrees celcius or 212 degrees fahrenheit. Whatever the name after the degrees, the fact remains that the water will be boiling!
In the same breath, a circle is a circle whether you give it 360 or 1,000 degrees – perhaps you could call yours 1,000 “degrees-mwangi” and mine, “degrees kihanya"!
Nevertheless, there are many theories that try to explain how a circle ended up with 360 degrees. The one I like most says it has something to do with the number of days in a year.
According to this theory, early astronomers observed that stars appear to move around the earth in a cycle that lasts one year. Without using any equipment, they concluded that the duration was 360 days. Since they thought that the stars are moving around the Earth in a circular orbit, it was only natural to subdivide a circle 360 times – that is 360 degrees of an acr.
I like this theory because, in modern astronomy, degrees are further subdivided into minutes and seconds of arc – arcminutes and arcseconds, respectively. One degree has 60 arcminutes and one acrminute has 60 arcseconds.
Another delectable theory says that 360 was chosen because it is very easy to divide without leaving remainders: It has 24 divisors!
What the origin, degrees are actually a cumbersome way of measuring angles. A more convenient unit is the radian. This one makes use of the two basic parameters of a circle – the circumference and the radius. Thus the size of and angle in radians is the ratio of the length of an arc to the radius.
Now suppose the radius of certain circle is R; its circumference will be 2 x pi x R. Thus the ratio of circumference to radius is 2-pi. Therefore, the full circle has 2-pi radians, that is, 6.283radians.
It might seem unwise to use an irrational quantity like pi (whose exact value cannot be known!), but in mathematics, radians turnout to be a lot more convenient than degrees.
As an example, by straightforward division, it turns out that one radian is equal to approximately 57.296 degrees – a seemingly awkward value. But when you think it over, one radian is a rather convenient angle. It marks out an arc whose length is exactly equal to the radius of the circle. Clever, isn’t it?
 |
 |