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In article <19972183.1162327554453.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Magnus <maol9883@xxxxxxxxxxxxx> wrote:
Please quote the message you are replying to for context.
>To clarify my question. I don't understand why there are samples
>giving imaginary distances when they are real themselves as is the
>function.
You are NOT getting "imaginary distances". What you are getting is
imaginary solutions to the auxiliary equation
dr(x)/dx = 0
(i.e., to the cubic equation that defines the DERIVATIVE of the
distance).
Since the derivative of r(x) with respct to x is a cubic, it has
either 1 or 3 real roots. In some cases, you will get 3 critical
points (when all roots are real; possibly repeated), and in some cases
you will get only 1 critical point (when one root is real and two are
complex). But these are not "imaginary distances" by any stretch.
--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org
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