A137616 Decimal expansion of surface area of the Meissner Body.

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

Offset

1,1

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), S. 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.

Links

Table of n, a(n) for n=1..101.

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).

Formula

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

Example

2.93411519432335593899268892412301181446158693642737...

Mathematica

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

Crossrefs

Cf. A102888, A137615, A137617, A137618.

Sequence in context: A071194 A347359 A346839 * A154581 A111689 A085093

Adjacent sequences: A137613 A137614 A137615 * A137617 A137618 A137619

Keyword

cons,easy,nonn

Author

Christof Weber, Feb 04 2008

Extensions

Link corrected by Christof Weber, Jan 06 2013

Status

approved