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Re: decimal point/comma (was conplaneteering)

From:Mark J. Reed <markjreed@...>
Date:Sunday, February 20, 2005, 16:32
On Mon, Feb 21, 2005 at 12:27:48AM +1100, Tristan McLeay wrote:
> rad is just the SI symbol > for radians, like g for grams, so it's not technically an abbreviation, > any more than an Omega is an abbreviation for Ohm
In my usage, it's an abbreviation. I didn't know the SI had an official symbol for radians. :)
> I'm not entirely sure I understand unitless quantities.
Unitless quantities express a simple multiplier/ratio factor; they have no units because the units cancel out. Radians are fundamentally arc length (on the perimeter of a circle) divided by radius (of the same circle). That is, an angle of one radian is the angle which subtends, on the perimeter of the circle, an arc length equal to the circle's radius. When you divide length by length, the units cancel; it doesn't matter if it's cm over cm, or m over m, or inches over inches, or miles over miles; the result is a bare number.
> I understand that decibels (or rather, bels) > are unitless quantities, does that mean that there should be a > relationship between bels and radians? and so you can say: that angle > is x bels, or: that noise was y radians?
Well, bels aren't really unitless, because they represent values on a logarithmic scale. You have to expand them to get a simple factor. 1 bel = 10, 2 bels = 100, etc. It's true, however, that the exponentiation is *all* that "bel" means; it's effectively a named unit for "ten to the power of", and there's nothing about its value which ties it to measuring sound. You could certainly say that a right angle is 2 decibel radians, for instance.
> I'm under the impression that the closest thing that exists to a metric > degree of angle is radians themselves.
You misunderstand me. The SI unit of angle measure is indeed the radian. Grads were, however, part of the French metric system at one point, which predates SI, and are "metric" in that historical sense; also, at least in America we use "metric" as a more general adjective applicable to any system of measurement units based on powers of 10. (There are exactly 100 grads in a quadrant).
> On a tangent
Speaking of angles! :)
> With the conventional measurements of temperature, such as degrees > Celsius and degrees Fahrenheit, you have the modifier after the noun > 'degree/s', and the modifier does not change. Colloquially, one can > drop the 'degrees' for scales not commonly used: hence I might talk > about 'thirty-eight degrees' and 'ninety-eight Fahrenheit'. Kelvin, the > proper SI temperature measurement, does not take 'degrees',
...any longer. It was originally "degrees Kelvin".
> and looks > like just any other SI measurement. So does one say 'thirty-eight > kelvin' (by analogy with 'ninety-eight Fahrenheit) or 'thirty-eight > kelvins' (by analogy with 'sixty-two metres'), correctly?
The latter; e.g. The triple point of water is 273.16 kelvins, and is defined so, with plural morpheme, in the SI spec. -Marcos