In article <ln8w22euvp....@nuthaus.mib.org>, Keith Thompson <ks...@mib.org> wrote:
> "BartC" <b...@freeuk.com> writes: > > "RG" <rnospa...@flownet.com> wrote in message > > news:rnospamon-20651e.17410012102...@news.albasani.net... > [...] > >> Likewise, all of the following are the same number written in different > >> notations: > >> > >> pi/2 > >> pi/2 radians > >> 90 degrees > >> 100 gradians > >> 1/4 circle > >> 0.25 circle > >> 25% of a circle > >> 25% of 2pi > >> > >> See? > > > > But what exactly *is* this number? Is it 0.25, 1.57 or 90? > > It's approximately 1.57. > > > I can also write 12 inches, 1 foot, 1/3 yards, 1/5280 miles, 304.8 mm and > > so > > on. They are all the same number, roughly 1/131000000 of the polar > > circumference of the Earth. > > They aren't bare numbers, they're lengths (actually the same length). > > > This does depend on the actual size of an arbitrary circle, but that seems > > little different from the choice of 0.25, 1.57 or 90 for your quarter > > circle. > > The radian is defined as a ratio of lengths. That ratio is the same > regardless of the size of the circle. The choice of 1/(2*pi) of the > circumference isn't arbitrary at all; there are sound mathematical > reasons for it. Mathematicians could have chosen to set the full > circumference to 1, for example, but then a lot of computations > would contain additional multiplications and/or divisions by 2*pi. http://www.math.utah.edu/%7Epalais/pi.pdf rg -- http://mail.python.org/mailman/listinfo/python-list
