A137617 Decimal expansion of volume of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes.

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

Offset

0,1

Comments

The rotated Reuleaux triangle is not only a body of constant width, it is the minimum volume surface of revolution with constant width (Campi et al. 1996).

References

St. Campi, A. Colesanti and P. Gronchi, Minimum problems for volumes of convex bodies, Partial Differential Equations and Applications - Collected Papers in Honor of Carlo Pucci, Marcel Dekker (1996), pp. 43-55.

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 informations on bodies of constant width like the rotated Reuleaux Triangle and others)

Formula

2/3 * Pi - Pi^2 / 6

Example

0.44946103...

Mathematica

k1[x_] := Sqrt[1 - (x - Sqrt[3]/2)^2]; k2[x_] := Sqrt[1 - x^2] - 1/2; Pi * Integrate[k1[x]^2, {x, Sqrt[3]/2 - 1, 0}] + Pi * Integrate[k2[x]^2, {x, 0, Sqrt[3]/2}]

Crossrefs

Cf. A102888, A137615, A137616, A137618.

Sequence in context: A283919 A283670 A019627 * A345732 A023405 A160900

Adjacent sequences: A137614 A137615 A137616 * A137618 A137619 A137620

Keyword

cons,easy,nonn

Author

Christof Weber, Feb 04 2008

Extensions

Link corrected by Christof Weber, Jan 06 2013

Status

approved