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

$$\alpha={\sin(rA)\over\sin(r-rA)}.$$

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

References

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.'' http://cedar.evansville.edu/~ck6/tcenters/recent/hofstad.html.