Geodesic
Two Kinds of Golden Triangles, Generalized to Match Continued Fractions
Journal for geometry and graphics, Tome 11 (2007) no. 2, pp. 165-171 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M04
Mots-clés : Golden triangle, golden ratio, continued fraction 
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     author = {C. Kimberling },
     title = {Two {Kinds} of {Golden} {Triangles,} {Generalized} to {Match} {Continued} {Fractions}},
     journal = {Journal for geometry and graphics},
     pages = {165--171},
     year = {2007},
     volume = {11},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a1/}
}
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C. Kimberling . Two Kinds of Golden Triangles, Generalized to Match Continued Fractions. Journal for geometry and graphics, Tome 11 (2007) no. 2, pp. 165-171. http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a1/