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geom3d[HarmonicConjugate] - Find the harmonic conjugate of a point with respect to two other points
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Calling Sequence
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HarmonicConjugate(A, B, C, F)
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Parameters
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A
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name
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B, C, F
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three points
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Description
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The routine returns A which is the harmonic conjugate of F with respect to B and C.
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If A, B, C, F are four collinear points such that the cross-ratio(AF, BC) = -1 (so that B and C divide AF one internally and the other externally in the same numerical ratio), the segment AF is said to be divided harmonically by B and C. The points A and F are called harmonic conjugates of each other with respect to B and C, and the four points A, F, B, C are said to constitute a harmonic range.
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The command with(geom3d,HarmonicConjugate) allows the use of the abbreviated form of this command.
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Examples
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![[63/17, 63/17, 0]](/support/helpjp/helpview.aspx?si=5922/file03977/math127.png)
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check that the harmonic conjugate of A with respect to BC is the same as F
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Download Help Document
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