Geodesic
Two Kinds of Golden Triangles, Generalized to Match Continued Fractions
Journal for geometry and graphics, Tome 11 (2007) no. 2, pp. 165-171.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 
@article{JGG_2007_11_2_JGG_2007_11_2_a1,
     author = {C. Kimberling },
     title = {Two {Kinds} of {Golden} {Triangles,} {Generalized} to {Match} {Continued} {Fractions}},
     journal = {Journal for geometry and graphics},
     pages = {165--171},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a1/}
}
TY  - JOUR
AU  - C. Kimberling 
TI  - Two Kinds of Golden Triangles, Generalized to Match Continued Fractions
JO  - Journal for geometry and graphics
PY  - 2007
SP  - 165
EP  - 171
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a1/
ID  - JGG_2007_11_2_JGG_2007_11_2_a1
ER  - 
%0 Journal Article
%A C. Kimberling 
%T Two Kinds of Golden Triangles, Generalized to Match Continued Fractions
%J Journal for geometry and graphics
%D 2007
%P 165-171
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a1/
%F JGG_2007_11_2_JGG_2007_11_2_a1
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/