A137615 Decimal expansion of volume of the Meissner Body.

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

Offset

0,1

Comments

The Meissner body is a three-dimensional generalization of the Reuleaux triangle having constant width 1. Although it is based on the Reuleaux tetrahedron, it is different from that. The Meissner body exists in two different versions.

References

Johannes Boehm and E. Quaisser, Schoenheit und Harmonie geometrischer Formen - Sphaeroformen und symmetrische Koerper, Berlin: Akademie Verlag (1991), p. 71.

G. D. Chakerian and H. Groemer, Convex Bodies of Constant Width, in: P. Gruber and J. Wills (Editors), Convexity and its Applications, Basel / Boston / Stuttgart: Birkhäuser (1983), p. 68.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.10 Reuleaux Triangle Constants, p. 513.

Links

Table of n, a(n) for n=0..100.

Bernd Kawohl and Christof Weber, Meissner's Mysterious Bodies, Mathematical Intelligencer, Volume 33, Number 3, 2011, pp. 94-101.

SwissEduc: Teaching and Learning Mathematics, Bodies of Constant Width (with information, animations and interactive pictures of both Meissner bodies)

Eric Weisstein's MathWorld, Reuleaux Triangle.

Formula

Equals (2/3 - sqrt(3)/4 * arccos(1/3))* Pi.

Example

0.41986004596508022334213000096833827916507033508865...

Mathematica

RealDigits[(2/3 - Sqrt[3]/4 * ArcCos[1/3])* Pi, 10, 120][[1]] (* Amiram Eldar, May 27 2023 *)

Crossrefs

Cf. A102888, A137616, A137617, A137618.

Sequence in context: A105495 A256831 A010644 * A021990 A182545 A084887

Adjacent sequences: A137612 A137613 A137614 * A137616 A137617 A137618

Keyword

cons,easy,nonn

Author

Christof Weber, Feb 04 2008

Status

approved