subexpressions (OT: math)

[Steve Howell]

--- Steven D'Aprano
<steve at REMOVE.THIS.cybersource.com.au> wrote:

> On Sat, 02 Jun 2007 05:54:51 -0700, Steve Howell
> wrote:
> 
> >> 
> >>    def f(x): y = x*x; return sin(y)+cos(y);
> >> 
> > 
> > Although I know valid trigonometry is not the
> point of
> > this exercise, I'm still trying to figure out why
> > anybody would ever take the square of an angle. 
> > What's the square root of pi/4 radians?
> 
> Approximately 0.886 radians. It corresponds to the
> angle of a point on the
> unit circle quite close to (sqrt(2/5), sqrt(3/5)),
> or if you prefer
> decimal approximations, (0.632, 0.775).
> 
> Angles are real numbers (in the maths sense), so
> sqrt(pi/4) radians is
> just as reasonable an angle as pi/4 radians. Both
> are irrational numbers
> (that is, can't be written exactly as the ratio of
> two integers).
> 

Yes, I understand that, but what is the geometrical
meaning of the square root of an arc length?  And what
would the units be?  If you take the square root of an
area, the units change from acres to feet, or from
square meters to meters.




       
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