Find the harmonic conjugate of a point with respect to two other points - Maple Help

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geom3d[HarmonicConjugate] - Find the harmonic conjugate of a point with respect to two other points

Calling Sequence

HarmonicConjugate(A, B, C, F)

Parameters

A

-

name

B, C, F

-

three points

Description

• 

The routine returns A which is the harmonic conjugate of F with respect to B and C.

• 

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.

• 

The command with(geom3d,HarmonicConjugate) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

pointB,3,3,0,pointC,7,7,0,pointF,2111,2111,0:

HarmonicConjugateA,B,C,F

A

(1)

coordinatesA

6317,6317,0

(2)

check that the harmonic conjugate of A with respect to BC is the same as F

HarmonicConjugateF1,B,C,A

F1

(3)

AreDistinctF,F1

false

(4)

See Also

geom3d[AreConjugate]


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