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

Author

Christof Weber, Feb 04 2008

Keywords

• cons
• easy
• nonn

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.

Examples

			0.41986004596508022334213000096833827916507033508865...
		

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

• 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.

Crossrefs

Cf. A102888, A137616, A137617, A137618.

Programs

Mathematica

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

Formula

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