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Topic: [HM] Harmonic Circles?
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Clark Kimberling

Posts: 20
Registered: 12/3/04
[HM] Harmonic Circles?
Posted: Feb 26, 2000 10:42 AM
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Suppose W,X,Y,Z are collinear and |WY|/|XY| = |WZ|/|XZ|. Then, by
definition, {Y,Z} are harmonic conjugates wrt {W,X}. Now remove the
requirement that Y be collinear with W,X. Then, as is well known, the
locus of Z satisying the equation is a circle. One might call it the
harmonic circle of Y wrt {W,X}. However, these circles have
interesting properties, so possibly they already have a name, perhaps
in one of the classics of John Casey. Has someone encountered these
circles in the literature?

Changing the subject, I thank some of you who responded to inquiries
about H. C. Gossard (for whom the Gossard Perspector is named), "a
fruitful theorem," and "Hirst inverse." Your contributions are
acknowledged in the new Encyclopedia of Triangle Centers - ETC, at .

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