Harmonic Conjugate Points
Given Collinear points 
, 
, 
, and 
, and are harmonic conjugates with respect to and if
The distances between such points are said to be in Harmonic Ratio, and the Line Segment depicted above iscalled a Harmonic Segment.
Harmonic conjugate points are also defined for a Triangle.If and have Trilinear Coordinates 
and
, then the Trilinear Coordinates of the harmonic conjugates are
(Kimberling 1994).See also Harmonic Range, Harmonic Ratio
References
Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994. Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 13-14, 1990. Phillips, A. W. and Fisher, I. Elements of Geometry. New York: American Book Co., 1896. Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. New York: Viking Penguin, p. 92, 1992.
- Bowditch Curve
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