Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal for Geometry and Graphics 11 (2007), No. 2, 165--171Copyright Heldermann Verlag 2007 Two Kinds of Golden Triangles, Generalized to Match Continued Fractions Clark Kimberling Dept. of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, U.S.A. ck6@evansville.edu [Abstract-pdf] Two kinds of partitioning of a triangle $ABC$ are considered: side-partitioning and angle-partitioning. Let $a = |BC|$ and $b = |AC|$, and assume that $0< b \leq a$. Side-partitioning occurs in stages. At each stage, a certain maximal number $q_n$ of subtriangles of $ABC$ are removed. The sequence $(q_n)$ is the continued fraction of $a/b$, and if $q_n=1$ for all $n$, then $ABC$ is called a side-golden triangle. In a similar way, angle-partitioning matches the continued fraction of the ratio $C/B$ of angles, and if $q_n=1$ for all $n$, then $ABC$ is called a angle-golden triangle. It is proved that there is a unique triangle that is both side-golden and angle-golden. Keywords: Golden triangle, golden ratio, continued fraction. MSC: 51M04 [ Fulltext-pdf  (131  KB)] for subscribers only.