On 13/10/2010 02:36, Keith Thompson 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.
Being able to 'tag' values can help in some cases, much like the idea
of 'tainting' user input and having that taint propagate until it's
explicitly cleaned. Being able to tag a value as 'radians' can be
helpful. Consider the original purpose of Hungarian notation.
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