Golden Rhombus
المؤلف:
Kabai, S
المصدر:
Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant
الجزء والصفحة:
...
17-2-2020
1108
Golden Rhombus
A golden rhombus is a rhombus whose diagonals are in the ratio 
, where 
is the golden ratio.
The faces of the acute golden rhombohedron, Bilinski dodecahedron, obtuse golden rhombohedron, rhombic hexecontahedron, and rhombic triacontahedron are golden rhombi.
The half-angle 
is given by
(OEIS A195693).
Labeling the smaller interior angle as 
and the larger as 
, then
 |
(5)
|
and
(OEIS A105199 and A137218).
The diagonal lengths of a golden rhombus with edge length 
are given by
(OEIS A121570 and A179290), the inradius by
 |
(26)
|
and the area by
 |
(27)
|
REFERENCES:
Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, pp. 177, 179, and 187, 2002.
Sloane, N. J. A. Sequences A105199, A121570, A137218, A179290, and A195693 in "The On-Line Encyclopedia of Integer Sequences."
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