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Hofstadter Point

The $r$-Hofstadter Triangle of a given Triangle $\Delta ABC$ is perspective to $\Delta ABC$, and the Perspective Center is called the Hofstadter point. The Triangle Center Function is


As $r\to 0$, the Triangle Center Function approaches

\alpha={A\over a},

and as $r\to 1$, the Triangle Center Function approaches

\alpha={a\over A}.

See also Hofstadter Triangle


Kimberling, C. ``Hofstadter Points.'' Nieuw Arch. Wiskunder 12, 109-114, 1994.

Kimberling, C. ``Major Centers of Triangles.'' Amer. Math. Monthly 104, 431-438, 1997.

Kimberling, C. ``Hofstadter Points.''

© 1996-9 Eric W. Weisstein