subexpressions (OT: math)

[Cameron Laird]

In article <4662675b$1_5 at news.bluewin.ch>,
Leonhard Vogt  <leonhard.vogt at gmx.ch> wrote:
>>> Yes, I understand that, but what is the geometrical
>>> meaning of the square root of an arc length?  
>> 
>> That's a different question to your original question, which was asking
>> about the square root of an angle.
>> 
>>> And what would the units be?  
>> 
>> Angles are a ratio of two lengths, and are therefore dimensionless units.
>> So the square root of an angle is just another angle, in the same units,
>> and it requires no special geometric interpretation: the square root of 25
>> degrees (just an angle) is 5 degrees (just another angle). 
>
>But sqrt(25°) = sqrt(25/180*pi) = 5*sqrt(180/pi) != 5°
>
>Leonhard

Yes it is; that is, if you're willing to countenance the square root
of an angle at all, then there should be no problem swallowing
    
    sqrt(pi radians / 180) = 1 sqrt(degree)

so that

    sqrt(25 degrees) = sqrt(25) * sqrt(pi radians / 180)
     
		     = 5 * sqrt(degree)

If it helps, we can call

    zilth := sqrt(pi radians / 180)

Measured in square-roots of a degree, a zilth is numerically 1.