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A270230
Decimal expansion of 3/(4*Pi).
1
2, 3, 8, 7, 3, 2, 4, 1, 4, 6, 3, 7, 8, 4, 3, 0, 0, 3, 6, 5, 3, 3, 2, 5, 6, 4, 5, 0, 5, 8, 7, 7, 1, 5, 4, 3, 0, 5, 1, 6, 8, 9, 4, 6, 8, 6, 1, 0, 6, 8, 4, 6, 7, 3, 1, 2, 1, 5, 0, 1, 0, 1, 6, 0, 8, 8, 3, 4, 5, 1, 9, 6, 4, 5, 1, 3, 3, 9, 8, 0, 2, 6, 3, 5, 1, 7, 0, 7, 0, 4, 1, 4, 9, 3, 7, 9, 6, 2, 8, 9, 3, 4, 1, 0, 9
OFFSET
0,1
COMMENTS
Consider generic prisms with triangular bases (tp), enclosed by a sphere, and let f(tp) be the fraction of the sphere volume occupied by any of them (i.e., the ratio of the prism volume to the sphere volume). Then this constant is the supremum of f(tp). It is attained by prisms which have as their base equilateral triangles with edge lengths r*sqrt(2), and rectangular side faces that are r*sqrt(2) wide and r*2/sqrt(3) high, where r is the radius of the enclosing, circumscribed sphere.
An intriguing fact is that the volume of such a best-fitting prism is exactly r^3. Hence, 1/a is the volume of a sphere with radius 1.
Examples of similar constants obtained for other shapes enclosed by spheres are: A020760 for cylinders and A165952 for cuboids.
EXAMPLE
0.238732414637843003653325645058771543051689468610684673121501016...
MATHEMATICA
First@ RealDigits[N[3/4/Pi, 120]] (* Michael De Vlieger, Mar 15 2016 *)
PROG
(PARI) 3/4/Pi
CROSSREFS
Cf. A002193, A019699 (one tenth of 1/a), A020760, A020832 (one tenth of 2/sqrt(3)), A165952.
Sequence in context: A036970 A110144 A327353 * A265366 A265365 A183141
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 13 2016
STATUS
approved