"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. -- Keith Thompson (The_Other_Keith) ks...@mib.org <http://www.ghoti.net/~kst> Nokia "We must do something. This is something. Therefore, we must do this." -- Antony Jay and Jonathan Lynn, "Yes Minister" -- http://mail.python.org/mailman/listinfo/python-list
