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CTK Exchange
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ociem
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Aug-12-07, 01:29 AM (EST) |
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2. "RE: product of distances"
In response to message #1
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Thanks. I think the lemniscate may be a special case of this. The wolfram site shows it as a cross section of a torus. This makes sense based on what I had found imperically. I plotted one of these curves, but it was one continuous figure. It must have been closer to the edge of the torus. This is a great site. I'm sure I'll be back. |
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mpdlc
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Aug-12-07, 06:55 AM (EST) |
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3. "RE: product of distances"
In response to message #2
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Actually the lemniscate is a particular case of Cassini Ovals. It is easy to write the general analytical equation for these curves assuming both points C1 and C2 on X axis at same distance of origin O. Then their coordinates are C1 (c, 0) and C2 (-c, 0), calling just for convenience the produt of distance a^4. It can be write immediately the equation expressing the constant product of the distance to them from a generic point P(x,y)((x-c)^2 + y^2) ((x+c)^2 + y^2) = a^4. If c = a we have the classic lemniscate of Bernoulli, otherwise we obtain the Ovals that probably will explain your other results
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