subexpressions (OT: math)

Steven D'Aprano steve at
Sun Jun 3 12:05:17 CEST 2007

On Sun, 03 Jun 2007 09:02:11 +0200, Leonhard Vogt wrote:

>> 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°

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.


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