Dear Jim,
Thanks for the reference. That solves one of my problems; the radian
is listed as a part of the SI, but it does not begin to solve the
second issue.
It seems to me that there is a great gaping hole in the SI as long as
it does not have a simple easy to use method for angle measurement for
everyday practical applications.
I cannot see that a builder of a table (say) will look at his work and
remark, 'That leg looks like it's at the right angle — it's exactly
π/2 radians,' or 'the corner of this hexagonal room looks OK at 2π/3
radians'.
While the everyday users of angles (builders, sailors, air pilots,
astronomers, surveyors, etc.) perceive that the SI does not have a
unit for measuring angles quickly and easily, then the SI will be
(probably mostly unconsciously) perceived as fundamentally flawed.
I won't dwell on this issue. I agree with Pierre Abbat that I don't
think that radians are going to go away any time soon. But I do think
it's worthwhile occasionally to raise the thought of this rather
largish hole in the structure of the SI. My suggestion about quads
(symbol q) and milliquads (symbol mq) is just one suggestion to add to
the many available solutions.
Cheers,
Pat Naughtin
Geelong, Australia
On 2009/03/24, at 11:37 PM, James R. Frysinger wrote:
The radian is one of the 22 "Coherent derived units in the SI with
special names and symbols" (SI Brochure, Table 3).
Jim
Pat Naughtin wrote:
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 <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
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(C) 931.212.0267
(H) 931.657.3107
(F) 931.657.3108
Cheers,
Pat Naughtin
PO Box 305 Belmont 3216,
Geelong, Australia
Phone: 61 3 5241 2008
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