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 -- http://mail.python.org/mailman/listinfo/python-list
