Grad System and Units of Measurement

Date: 08/11/98 at 14:13:53
From: Greg MacNeill
Subject: Grad units of measurement

Hi,

I am having trouble finding information on one mode of operation for a 
simple scientific calculator. Typically three systems of measurement 
are provided: deg, rad and grad, which I assume represent degree, 
radian and grad. As I understand, the grad system is commonly used in 
Scandinavia and other northern European countries, particularly in 
mapping.

How does the grad system compare to the degree system? Is it true that 
the grad coordinate system is entirely consistent with metric 
measurement? Apparently grad units of arc are directly related to the 
metric linear equivalent. This is not the case of course with degrees 
except in nautical applications where 1 minute of arc equals 1 
nautical mile on the surface of the earth.

To achieve uniformity, perhaps we should measure all distances in 
nautical miles or adopt the grad system for angle measurement.

Please let me know what you can about the basics of grad measurement.

Thanks,
Greg

Date: 08/14/98 at 15:39:27
From: Doctor Schwa
Subject: Re: Grad units of measurement

Grads are defined to be 100 in a right angle, for people who are 
obsessed with the decimal system. Grad units of arc are related to the 
metric system only in that way: a multiple of 10 is used in their 
definition. 

The original definition of kilometer was that there are 10,000 of 
them between the equator and the north pole, so that 1 grad = 100 km, 
1 centigrad = 1 km, would indeed be convenient for mapping in much the 
same way as 1 minute = 1 nautical mile is. But of course that's just an 
approximation - among other things, the Earth isn't particularly close 
to a perfect sphere.

I side with the Babylonians - the convenience of 90 degrees being 
evenly divisible by all kinds of things (most notably 3, which makes 
the 30-60-90 triangle so easy to talk about) is well worth it.

- Doctor Schwa, The Math Forum
Check out our web site! http://mathforum.org/dr.math/