subexpressions (OT: math)

[Gary Herron]

Stebanoid at gmail.com wrote:
> On 3    , 14:05, Steven D'Aprano <s... at REMOVE.THIS.cybersource.com.au>
> wrote:
>   
>> On Sun, 03 Jun 2007 09:02:11 +0200, Leonhard Vogt wrote:
>>     
>>>> bla-bla
>>>>         
>> Hmmm... perhaps that's why the author of the "units" program doesn't
>> treat angles as dimensionless when taking square roots.
>>
>> Given that, I withdraw my claim that the sqrt of an angle is just an
>> angle. I can't quite see why it shouldn't be, but the evidence is fairly
>> solid that it isn't.
>>
>> --
>> Steven
>>     
>
> angle is dimensionless unit.
>   
Of course not!  Angles have units, commonly either degrees or radians.

However, sines and cosines, being ratios of two lengths, are unit-less.
> To understand it: sin() can't have dimensioned argument. It is can't
> to be - sin(meters)
>   
No it's sin(radians) or sin(degrees). 
> it is difficult to invent what is a "sqrt from a angle" but it can be.
>   
I don't know of any name for the units of "sqrt of angle", but that
doesn't invalidate the claim that the value *is* a dimensioned
quantity.  In lieu of a name, we'd have to label such a quantity as
"sqrt of degrees" or "sqrt of radians".      After all, we do the same
thing for measures of area.  We have some units of area like "acre", but
usually we label areas with units like  "meters squared" or "square
meters".    That's really no stranger than labeling a quantity as "sqrt
of degrees".

Gary Herron, PhD.
Department of Computer Science
DigiPen Institute of Technology