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Re: Re: Re: Solve or Reduce?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64450] Re: [mg64412] Re: [mg64398] Re: Solve or Reduce?
*From*: "David Park" <djmp at earthlink.net>
*Date*: Fri, 17 Feb 2006 04:12:14 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
The following table gives the solutions in degrees as a varies from 0 to 90
degrees. Each triplet is {a, first b solution, second b solution}. Because
the RootSearch routine I was using gives the results in sorted order, the
two roots switch columns at 60 degrees.
{{0, 0., 277.628},
{5, 8.14157, 279.009},
{10, 16.3816, 281.034},
{15, 24.8218, 283.798},
{20, 33.5778, 287.445},
{25, 42.7897, 292.171},
{30, 52.6316, 298.233},
{35, 63.3125, 305.928},
{40, 75.0545, 315.54},
{45, 88.0132, 327.201},
{50, 102.111, 340.683},
{55, 116.839, 355.264},
{60, 9.92425, 131.266},
{65, 23.8027, 144.4},
{70, 36.4951, 155.625},
{75, 47.9915, 164.805},
{80, 58.473, 172.123},
{85, 68.1628, 177.873},
{90, 77.2632, 182.348}}
There are always two solutions and they are perfectly well behaved.
Those who have the Cardano3 complex graphics package, and Ted Ersek's
RootSearch package and who are interested in the solution, and animations of
the solution, may contact me and I will send them the solution notebook,
CirclesGeometry.nb.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Math Novice [mailto:math_novice_2 at yahoo.com]
To: mathgroup at smc.vnet.net
I am trying to find the angle b corresponding to the points on the
circumference of the circle (5+8 Cos[b], 7+8 Sin[b]) that are a distance of
7 units from a point on the circumference of the circle (13 cos[a], 13
Sin[a]) for angles a in the first quadrant. (5+8 Cos[b], 7+8 Sin[b]) is a
circle of radius 8 and center (5,7) and (13 cos[a], 13Sin[a]) is a circle of
radius 13 and center (0,0).
(13,0) on the circle (13 cos[a], 13 Sin[a]) and (13,7) on (5+8 Cos[b], 7+8
Sin[b]) are the first set of points that are 7 units apart when the angle a
(of the larger circle ) is equal to 0. As I increase the value of a and use
my compass (set at 7 units) to measure on the printout of the diagram of the
two circles it seems that there should always be an angle for b that
corresponds to a and b should always increase as a increases but something
happens at about 32 degrees. For some calculations b starts to decrease as a
increases past 32 degrees or with some other calculations b becomes negative
as a increases past 32 degrees. Any idea of what I?m going wrong?
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