subexpressions (OT: math)

[Lloyd Zusman]

"Steven D'Aprano" <steve at REMOVE.THIS.cybersource.com.au> writes:

> On Sun, 03 Jun 2007 11:26:40 -0700, Stebanoid at gmail.com wrote:
>
>> if you are discordant read more :P :
>> sine is a dimensionless value.
>> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
>> etc.
>> you can see that sin can be dimensionless only if x is dimensionless
>> too.
>> 
>> I am a professional physicist and a know about what I talk
>
> I am confused why you get different results for the square root of an
> angle depending on whether you use degrees or radians:
>
> sqrt(25°) = 5° = 0.087266462599716474 radians
> sqrt(25*pi/180) = 0.66055454960100179 radians
>
> If angles are dimensionless numbers, then:
>
> degrees_to_radians(sqrt(25°)) 
>
> should equal 
>
> sqrt(degrees_to_radians(25°))
>
> but they don't.

That's because for arbitrary functions f and g, 

  f(g(x)) is not equivalent to g(f(x))

This has nothing to do with whether or not x is a dimensionless number.

(replace "f" with "degrees_to_radians" and "g" with "sqrt")


-- 
 Lloyd Zusman
 ljz at asfast.com
 God bless you.