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AreHarmonic

  

test if a pair of points is harmonic conjugate to another pair of points

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AreHarmonic(A, B, C, F)

Parameters

A, B, C, F

-

four points

Description

• 

The routine returns true if C and F are harmonic conjugates of each other with respect to A and B; false if C and F are not harmonic conjugates; and FAIL if it cannot determine whether C and F are harmonic conjugates.

• 

If A, B, C, F are four collinear points such that the cross-ratio(AB,CF) = -1 (so that C and F divide AB one internally and the other externally in the same numerical ratio), the segment AB is said to be divided harmonically by C and F. The points C and F are called harmonic conjugates of each other with respect to A and B, and the four points A, B, C, F are said to constitute a harmonic range.

• 

The command with(geometry,AreHarmonic) allows the use of the abbreviated form of this command.

Examples

withgeometry:

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

AreHarmonicA,B,C,F

true

(1)

AreHarmonicB,A,C,F

true

(2)

AreHarmonicA,C,B,F

false

(3)

pointF,2111,a

F

(4)

AreHarmonicA,B,C,F

AreCollinear:   "hint: could not determine if 3*a-63/11 is zero"

Error, (in geometry:-CrossRatio) unable to determine if 3*a-63/11 is zero

From the above hint, we see that the condition for F to be conjugate harmonic of C is a = 21/11

a2111:

AreHarmonicA,B,C,F

true

(5)

See Also

geometry[CrossRatio]

geometry[SensedMagnitude]

 


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