In article <[EMAIL PROTECTED]>, Leonhard Vogt <[EMAIL PROTECTED]> 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.
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