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From: dmitry@elros.cbb-automation.de (Dmitry A. Kazakov)
Newsgroups: comp.lang.ada
Subject: Re: Another Idea for Ada 20XX
Date: Mon, 10 Dec 2001 09:01:17 GMT
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Date: 2001-12-10T09:01:17+00:00
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On Fri, 07 Dec 2001 22:51:47 GMT, "Mark Lundquist"
<mlundquist2@attbi.com> wrote:

>
>"Philip Anderson" <phil.anderson@amsjv.com> wrote in message
>news:3C0F8E75.4F5CB3B8@amsjv.com...
>> Mark Lundquist wrote:
>> >
>> <snip>
>> > Units are unlike types in that they are optional (think about it, what
>units
>> > would you give for Pi?).
>> <snap>
>>
>> I don't think units are "optional", although they may be dimensionless,
>> ie just numbers like Pi.
>
>Eh?  OK, so I'll ask again, what units would you give for Pi?
>
>>  Note that radians, being a ratio, are actually
>> dimensionless.
>
>No, they are not!
>
>(BTW rate is also the ratio of distance/time, and of course rate isn't
>dimensionless -- any more than radians are!)
>
>The dimension of angle is distance/distance.  (I'm not making this up -- the
>SI define radians in terms of meter*(meter**-1)). 

There are lot of formulae involving Pi, which you can derive Pi units
from. Consider formula of volume, or better Euler's -1= exp (j*Pi)
(:-)).

>That's why when you
>multiply a distance by an angle, you get a distance.  But if you were to
>multiply a mass by an angle, you do not get a mass (which would make it a
>unit conversion), but something whose units would be "kg-radians".  (What
>use would that have?  Beats me, for all I know there might be one... I'm a
>physics 'tard, my wise-ass PhD little brother got all the physics genes :-)
>:-)
>
>Dimensionless numbers do not change the units when you multiply them, that's
>the difference.  No measurement is dimensionless.

This includes dimensionless numbers as well. For instance, when we
count, the result is measured in fingers (:-)).

Regards,
Dmitry Kazakov