Re: Natural Eq'm of Cardioid
- From: Rodo <mattrodo@xxxxxxxxx>
- Date: 2 May 2007 04:30:51 -0700
On May 1, 11:52 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <gerry-9E8F09.11223702052...@xxxxxxxxxxxxxxxxxx>,
Gerry Myerson <g...@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In article <1178063837.566281.103...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Rodo <mattr...@xxxxxxxxx> wrote:
I'm having a difficult time with what is probably an easy problem.
The problem states:<br> "Consider the cardioid
r = 1 - cos(theta), 0 less than or equal to (theta) less than or
equal
to 2pi. Let s(theta) be the arc length from the point (2, pi) on the
cardioid to the point (r, theta) and let "rho" (theta) = 1 / K be the
radius of the curvature at the point (r, theta). Show that s and
"rho" (theta) are related by the equation s^2 + 9("rho")^2 = 16.
I haven't even the slighest clue where to begin with this. Any
insight is greatly appreciated!
Well, there's probably a formula somewhere for calculating
the arc length along a curve given in polar co-ordinates,
http://en.wikipedia.org/wiki/Arc_length
and there's probably a formula somewhere for calculating
the radius of curvature along a curve given in polar co-ords.
http://en.wikipedia.org/wiki/Curvature
I'd start by seeing what those formulas have to say about
your cardioid.- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text -
Thanks "Noone" and "Virgil" for your responses. I'm about to head to
class, but I'll see what I can come up with thanks to your extra
resources! Take Care.
-Rodo
.
- References:
- Natural Eq'm of Cardioid
- From: Rodo
- Re: Natural Eq'm of Cardioid
- From: Gerry Myerson
- Re: Natural Eq'm of Cardioid
- From: Virgil
- Natural Eq'm of Cardioid
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