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A211174 Johannes Kepler's polyhedron circumscribing constant. 2
1, 4, 2, 5, 2, 3, 2, 9, 2, 1, 5, 0, 1, 1, 3, 5, 6, 3, 9, 3, 9, 0, 4, 6, 2, 1, 8, 8, 8, 5, 1, 1, 0, 8, 3, 2, 8, 6, 2, 0, 6, 6, 0, 8, 5, 8, 0, 9, 7, 7, 6, 1, 0, 8, 8, 9, 3, 7, 1, 5, 4, 8, 7, 4, 7, 8, 3, 1, 8, 7, 0, 0, 1, 5, 5, 5, 8, 5, 3, 5, 4, 3, 1, 6, 2, 1, 6, 2, 1, 9, 4, 7, 5, 4, 5, 7, 5, 7, 1, 5, 1, 6, 4, 6, 5, 5, 8, 4, 8, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
The finite solid analogy to the plane polygon circumscribing constant (A051762).
The five Platonic solids are the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron and the icosahedron.
The geometric interpretation is as follows. Begin with a unit sphere. Circumscribe a tetrahedron and then circumscribe a sphere. Circumscribe a cube and then circumscribe a sphere. Circumscribe an octahedron and then circumscribe a sphere. Circumscribe a dodecahedron and then a sphere. Circumscribe an icosahedron and then a sphere. The constant is the radius of this last sphere. In actuality, it makes no difference the order of the five solids.
LINKS
Rüdiger Appel, 3Quarks: Platonic Solids (September 2010).
David A. Fontaine, The Five Platonic Solids.
George W. Hart, Virtual Polyhedra, 1998, Johannes Kepler's Polyhedra.
Omar E. Pol, Circunferencias concéntricas y polígonos regulares inscritos, gaussianos, Nov 17 2007, 13:17
Wikipedia, Platonic Solids.
Wikipedia, Johannes Kepler.
FORMULA
= 9*(15 - 6*sqrt(5)).
EXAMPLE
14.25232921501135639390462188851108328620660858097761088937154874783...
MATHEMATICA
RealDigits[ 9(15 - 6 * Sqrt[5]), 10, 111][[1]]
CROSSREFS
Cf. A051762.
Sequence in context: A275927 A072907 A250719 * A367574 A059833 A123152
KEYWORD
cons,nonn
AUTHOR
EXTENSIONS
Offset corrected by Rick L. Shepherd, Dec 31 2013
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)