On 2009/03/24, at 2:15 PM, James R. Frysinger wrote:
Yes, of course, mathematicians as well!
Jim
Pierre Abbat wrote:
On Monday 23 March 2009 18:59:03 James R. Frysinger wrote:
I don't think that radians are going to go away in either of our
lifetimes. It's one of the derived units that physicists and many
engineers are fond of.
Mathematicians too. All trigonometric functions are naturally
defined with the angle in radians.
In my work, angles are expressed in degrees, minutes, and seconds.
Why DMS instead of decimal degrees or gons I do not know, but they
are measured with a theodolite that divides the circle into some
large round integral number of parts. For expressing bearings and
azimuths, radians would not make sense; there would be an odd-sized
interval just before 0. But I have to use radians, because, on some
older maps, curves are labeled with radius and length but not angle
or delta. To figure the delta (those old curves are almost always
tangent at both ends), I divide the length by the radius. That's
the delta in radians. Then I add or subtract that to the starting
bearing, which is in DMS. So I convert the delta to DMS. I've done
this enough that I have a radian in seconds memorized. It's
206264.8, and its reciprocal is 4.848137e-6.
Pierre
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
Dear Jim and All,
Does anyone know the current status of the radian as an official SI
unit?
It looks like it was introduced into the SI, as a supplementary unit,
in 1960
(See http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=11&RES=12 )
And eliminated as a supplementary unit in 1995
(See http://www.bipm.org/en/CGPM/db/20/8/ )
According to this second reference, the radian 'may, but need not, be
used in expressions for other SI derived units, as is convenient'.
This poses two questions:
1 Is the radian an official SI unit? and
2 If the answer to my first question is negative, does the SI have a
unit for angles at all?
As you know from your knowledge of the history of the metric system,
the first unit of the decimal metric system in 1790 was the quadrant,
which was decimally divided into grades and centigrades and it was the
quadrant that was then used to make the measurements that defined the
metre. Let me stress this: the quadrant was the first unit of the
decimal metric system, the metre was the second, and all the rest
followed from there.
You may recall that I have worried about this issue in the past. It
appals me that the SI does not have a unit for angles that can be
conveniently used for designing and constructing buildings. There are
probably more angle measures done on the building sites of the world
than anywhere else in our societies. All that carpenters and plumbers
have — by default — is the old Babylonian degrees, minutes, and
seconds as radians have almost always been useless to them. My
recommendation some years ago was that the CIPM and the CGPM should
recognise that the initial unit of the metric system was the quadrant,
that this unit name could be reduced to the unit name quad, and that
and builders, sailors, and all of us could measure all of our angles
in quads (symbol q) and milliquads (symbol mq).
Cheers,
Pat Naughtin
PO Box 305 Belmont 3216,
Geelong, Australia
Phone: 61 3 5241 2008
Metric system consultant, writer, and speaker, Pat Naughtin, has
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