subexpressions (OT: math)
Steven D'Aprano
steve at REMOVE.THIS.cybersource.com.au
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.
--
Steven
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