I agree with your remaining point about the radian being impractical for
daily street-level use, Pat.
A few years ago I read an article in Metrologia in which the Barry
Taylor, et al. argued for equal status for the degree as a derived unit.
That did not make it into the 8th edition.
I have no bet down on the horse race degree vs. quad vs. gon. But the
degree horse is the only one I've ever ridden. Some might argue that the
degree is friendlier to "common" angles than the gon or the milliquad,
but then the argument about what is "common" starts up.
Jim
Pat Naughtin wrote:
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
<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
Metric system consultant, writer, and speaker, Pat Naughtin, has helped
thousands of people and hundreds of companies upgrade to the modern
metric system smoothly, quickly, and so economically that they now save
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--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(C) 931.212.0267
(H) 931.657.3107
(F) 931.657.3108
