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.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
EXAMPLE
0.238732414637843003653325645058771543051689468610684673121501016...
MATHEMATICA
First@ RealDigits[N[3/4/Pi, 120]] (* Michael De Vlieger, Mar 15 2016 *)
PROG
(PARI) 3/4/Pi
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 13 2016
STATUS
approved