Why Has Geometry Not Been 'metricked'? Why 360 Degrees Intstead ...

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David Hughes, Toronto, Canada

• 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?

  Peter Brooke, By Kinmuck Scotland

• It has been; there is the unit called the Grad of which 100 is a right angle (90 conventional degrees, or pi/2 radians). It originated in France as the 'grade' along with other metric units. I only know of the French artillery actually using it.

  Andrew Walker, Leicester, England

• In fact degrees have been "metricated", in engineering angles are often measured in radians, whereby the circumference of a circle is expressed as 2Π Radians.

  Angular measurement in degrees or radians is given in reference to a circle, 360 degrees or 2 Pi radians being the measure one full revolution. If we were to divide a circle into anything other than 360 deg we would have to change our calendars too - the ancient Greeks worked out that there were 360 days in the year, and that, therefore, we progress about the sun at one degree per day - they were quite close given that they worked on observation alone!

  Peter Clark, Cambridge, UK

• 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.

  Ray Gallagher, Belfast, Northern Ireland

• 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.

  Vivienne, London UK

• 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!

  Chris Lyes, Hungerford, UK

• 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.

  Tom Amies, Vancouver, Washington USA

• 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)

  Kamyar, Samos Greece

• 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.'

  Jonathan S., Hereford England

• The gradian, grade, grad or gon is a metric angular unit developed in post-revolutionary France as part of the metric system (along with 10 day weeks, 10 hour days, 100 minute hours and 100 second minutes). There are 100 grads in a right angle, or 400 grads in 360 degrees It is still in use by the French military and pocket calculators have degree, radian, and gradian modes for trigonometric functions.

  Mark Manzocchi, Aberdeen, UK

• Grads are used to a small extent in France and elsewhere. There are 100 grads to the right angle, 400 to the full circle. The calculator accessory that comes with the Windows operating system allows you to select working in grads rather than degrees or radians.

  Nick Rouse, Plumpton Green UK

• Whilst mathematicians are happy with degrees, or more usually radians as the maths gets more advanced, others have indeed split angles into 100. The gradian or grad is the unit of measurement which is obtained by splitting a right angle (90 degrees) into 100 parts. The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way. I imagine there are others in use - after all the 360 degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice.

  Hayden Rissbrook, Walthamstow, UK

• Whilst mathematicians are happy with degrees, or more usually gradians, as the maths gets more advanced, others have indeed split angles into 100. The gradian or grad is the unit of measurement which is obtained by splitting a right angle (90 degrees) into 100 parts. The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way. I imagine there are others in use, afterall the 360 degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice.

  Hayden Rissbrook, Walthamstow, UK

• 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.

  Lewis, London, UK

• The use of 400 gon instead of 360 degrees can also be found in land surveying as well. Some theodolites will have the option of degrees or gon and many that were made in the former eastern block used this system.

  Hamish, Ipswich, UK