Re: dimensionless units

[John Denker <jsd@MONMOUTH.COM>]

At 07:12 AM 11/29/00 -0500, David Abineri asked:
>  as to how radians, which are unit less, can be
> converted to degrees which are a specific unit.

The question contains a subtle but important misstatement.

At 09:13 AM 11/29/00 -0500, Wolfgang Rueckner wrote:
> Radians ARE units, just as degrees are.  They're dimensionless.

Exactly so.




The world is full of dimensionless units.  It is fun to go collecting
them.  Here is a start:

1) radian, steradian, degree, minute, second, grad

2) percent, ppm, ppb

3) Bel (as in deciBel), neper

4) bit, nat

5) Mach

How many more can you come up with?

=====================

There are also a lot of interesting things that are dimensionless but AFAIK
don't have a named unit to go with them.  These include

1) pH

2) Reynolds number, Nusselt number, Prandtl number et cetera

3) f/stop, numerical aperture

4) coefficient of friction

How many more can you come up with?

====================

It seems to me that the things on the second list can get by without named
units because there is a single, well-established, convenient-sized
unit.  If you ever get a situation where there are contending concepts
(e.g. Bel versus neper) somebody will coin names for the various
contenders.  Also when units have an inconvenient size, somebody will coin
a name just so we can hang metric prefixes on it (e.g. milliradian).