"Strong typing vs. strong testing" [OT]

[Steven D'Aprano]

On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:

>> The formula: circumference = 2 x pi x radius is taught in primary
>> schools, yet it's actually a very difficult formula to prove!
> 
> What's to prove?  That's the definition of pi.

Incorrect -- it's not necessarily so that the ratio of the circumference 
to the radius of a circle is always the same number. It could have turned 
out that different circles had different ratios. 

In fact, in the real world, this *is* the case -- as space-time is not 
flat except far away from any gravitational mass, classical geometry is 
only approximately valid for real circles.

Even in mathematics, there are spherical and hyperbolic geometries that 
doesn't assume that the angles in a triangle add to 180 degrees, or 
another way of putting it, that the ratio of circumference to radius is 
not necessarily pi.

http://mathforum.org/library/drmath/view/55021.html


-- 
Steven