Why has geometry not been 'metricked'? Why 360 degrees intstead of 1, 10, 100 or even 1000?
Because one of the essential varibales in geometry is the number three. For example, three being a factor of 180 means that an equilateral triangle has angles of 60 degrees. What would their angles be in a metric system?
The degree is an arbitrary unit; basically any division of a circle would work as a system of measurement. The degree has the advantage that 360 divides evenly by 2, 3, 4, 5, 6, 8, 9 & 10 making it easy to mentally calculate an angle; indeed this is the major advantage of all old imperial units. There is a more fundamental unit call the Radian. This is the angle subtended by an arc of a circle equal in length to its radius. Since the circumference of a circle is 2 x pi x radius one there are 2 pi, or 6.283, Radians in a circle. This is fine for calculations on angular motion but difficult to work out in your head.
We inherited 360 degrees from the Babylonians, but many ancient societies were highly interested in astronomy and in some (megalithic Britain?) had 366 degrees in a circle. This is logical, since the earth turns on its axis 366 times a year. Their measurements seem to have been interrelated and not arbitrary as a metrically divided circle would be. The Babylonians probably reduced this to 360 as it divides so much more easily by many factors.
When working on an archaeological dig near Rome, I was once given a theodolite to set up. After some time struggling to get it to work, I noticed that the scale on which horizontal angles were measured read 400 degrees rather than 360. My supervisor told me that this was and old piece of equipment, once part of an attempt to metricise the circle. I'm not sure whether this was purely an Italian initiative or not!
The Babylonians gave us the 360-degree circle. That number turns out to be the smallest one whose quotient is an integer when divided by any whole number from 1 through 10 (except for 7, which may have added to seven's stature as a "magic number". I've heard that (at least in the U.S. military), artillery batteries use a 1000-degree circle for more accuracy, so -- if true -- at least that's a start.
Both Babylonians and Chinese used sexagesimal system which means they had 59 figures rather than 9 (zero was invented much later). Although they did have a figure for 10 so their number 11 was still written as figure of 10 next to figure of 1. The origin of this is not known for sure although they were obviously influenced by astronomy and the fact that there are (almost) 360 days in a year. They also came up with sixty minutes in the hour, 24 hours a day. This is only another example of the slipping of school standards that we only expect school children to only know 9 figures (and zero)
Because you usually want to know how far round the circle you are, and you can divide 360 into many more useful fractions. Indeed, the unit favoured by mathematicians isn't the degree but the radian. Twice pi (6.2831853...) radians equals 360 degrees. So rather than 90 degrees you say 'pi-over-two radians.'
360 has many more divisors than 10, 100, 1000 etc. Therefore a circle can be divided more easily into many diferent equal parts - 2,3,4,5,6,8,9,10...... Try doing that with 100 or 1000.
http://www.guardian.co.uk/notesandqu...185569,00.html