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Geometry 189
lines; in this case, it returns the equation of the harmonic
conjugate line.
harmonic_conjugate(point1, point2, point3) or
harmonic_conjugate(line1, line2, line3)
Example:
harmonic_conjugate(point(0, 0), point(3, 0),
point(4, 0)) returns point(12/5, 0)
harmonic_division
Returns the harmonic conjugate of 3 points. Specifically,
returns the harmonic conjugate of point3 with respect to
point1 and point2 and stores the result in the variable var.
Also accepts three parallel or concurrent lines; in this case, it
returns the equation of the harmonic conjugate line.
harmonic_division(point1, point2, point3, var)
or harmonic_division(line1, line2, line3, var)
Example:
harmonic_division(point(0, 0), point(3, 0),
point(4, 0), p) returns point(12/5, 0) and stores it
in the variable p
is_harmonic
Tests whether or not 4 points are in a harmonic division or
range. Returns 1 if they are or 0 otherwise.
is_harmonic(point1, point2, point3, point4)
is_harmonic(point1, point2, point3, point4)
Example:
is_harmonic(point(0, 0), point(3, 0),
point(4, 0), point(12/5, 0)) returns 1
is_harmonic_circle_bundle
Returns 1 if the circles build a beam, 2 if they have the same
center, 3 if they are the same circle and 0 otherwise.
is_harmonic_circle_bundle({circle1, circle2,
…, circlen})