The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Inactive » Historia-Matematica

Topic: [HM] Harmonic Circles?
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Clark Kimberling

Posts: 20
Registered: 12/3/04
[HM] Harmonic Circles?
Posted: Feb 26, 2000 10:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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
http://cedar.evansville.edu/~ck6/encyclopedia/ .





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.