A349578 Decimal expansion of the volume of the solid formed by the intersection of 6 right circular unit-diameter cylinders whose axes are parallel to the face diagonals of a cube and intersect at a single point.

5, 3, 8, 1, 6, 4, 9, 1, 0, 4, 3, 0, 2, 4, 9, 5, 9, 4, 5, 6, 5, 4, 2, 5, 1, 9, 0, 7, 8, 1, 9, 6, 8, 2, 7, 9, 7, 3, 7, 9, 4, 8, 6, 7, 0, 7, 4, 1, 9, 7, 9, 3, 0, 8, 9, 3, 6, 5, 9, 6, 6, 7, 1, 2, 9, 3, 9, 5, 7, 4, 1, 3, 3, 1, 2, 7, 8, 1, 2, 7, 9, 1, 7, 3, 8, 2, 8, 1, 5, 7, 4, 6, 9, 2, 8, 7, 2, 4, 0, 2, 7, 4, 1, 3, 1

Offset

0,1

Comments

This constant was first calculated by Moore (1974).

Links

Table of n, a(n) for n=0..104.

Paul Bourke, Intersecting cylinders, 2003-2016.

Moreton Moore, Symmetrical Intersections of Right Circular Cylinders, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.

Eric Weisstein's World of Mathematics, Steinmetz Solid.

Wikipedia, Steinmetz solid.

Formula

Equals (2/3) * (3 + 2 * sqrt(3) - 4 * sqrt(2)).

Example

0.53816491043024959456542519078196827973794867074197...

Mathematica

RealDigits[(2/3) * (3 + 2 * Sqrt[3] - 4 * Sqrt[2]), 10, 100][[1]]

Crossrefs

Cf. A101465, A349577, A349579, A349580.

Sequence in context: A087654 A086032 A018222 * A388333 A392502 A374260

Adjacent sequences: A349575 A349576 A349577 * A349579 A349580 A349581

Keyword

nonn,cons

Author

Amiram Eldar, Nov 22 2021

Status

approved