subexpressions (OT: math)

[Steve Howell]

--- Peter Otten <__peter__ at web.de> wrote:
> 
> I know not much more about Fourier series than that
> they do exist, so let me
> refer you to
> 
> http://en.wikipedia.org/wiki/Fourier_series
> 

I'd like to try to bring this thread back full circle
(or maybe at least 7*pi/4).

   1) OP posted an example of sin(x*x) + cos(x*x).

   2) I posted the observation (slight paraphrase of
myself) that above formula looks like a high school
math mistake.

   3) I also asked for geometric interpretation of
square root of an arc length, not really expecting
one, although eventually somebody posted an
interesting physical interpretation (noise density).

   4) I also asked about units in general.  The
general consensus is that radians are dimensionless.

   5) Any exploration of trigonometry among smart
people eventually leads to Fourier Series expansions. 

   
Trying to bring this back to Python, I think Fourier
Series make a better example of a situation where you
end up repeating subexpressions:

lambda t: a[0]/2 + sum(a[n]*cos(n*f*t) +
b[n]*sin(n*f*t) \
    for n in range(1,101))

   


       
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