On 2012-12-17 20:05, Andre' Walker-Loud wrote:
>>> I reiterate that in polar coordinates, a negative value of "r"
>>> does not make sense. It is confusing at best.
>>
>> This isn't really true. Many standard introductions to polar
>> coordinates consider negative r as valid. It's simply treated as
>> a radius in the opposite direction
>
> In Euclidean space, can you have a negative distance? Would you
> ever describe a circle as having negative radius (in Euclidean
> space)? If you take "r" to be the radius, then I suggest you
> confuse a precise definition of radius with allowing a useful,
> non-unique interpretation of negative values of "r".
I don't take r to be "the radius", I take it to be a number in an
ordered pair with a particular mapping into R^2. It is an extension
of the notion of radius, but there's no reason it has to conform with
the restrictions on geometrically possible radii.
However, those issues are beside the point. The point is that,
regardless of what a radius is, in the context of polar coordinates, a
negative *r-coordinate* is a perfectly mathematically respectable
notion with a standard interpretation. Moreover, it is actually
useful when you want to graph some things, and is supported by other
plotting software (see, e.g.,
http://www.wolframalpha.com/input/?i=polar+plot+r%3Dtheta%2C-pi%3Cr%3C0).
Matplotlib should plot r-coordinates according to this standard
interpretation,
--
Brendan Barnwell
"Do not follow where the path may lead. Go, instead, where there is
no path, and leave a trail."
--author unknown
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