A137618 Decimal expansion of surface area of the solid of revolution generated by a Reuleaux triangle rotated around one of its symmetry axes.

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

Offset

1,1

Comments

The rotated Reuleaux triangle is not only a surface of constant width, it is the minimum area 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=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, Gleichdick - Koerper konstanter Breite (in German and English)

Formula

Equals 2*Pi - Pi^2 /3.

Example

2.99331717348313360398045643326695538995643899633661...

Mathematica

k1[x_] := Sqrt[1 - (x - Sqrt[3]/2)^2]; k2[x_] := Sqrt[1 - x^2] - 1/2; 2*Pi*Integrate[k1[x]*Sqrt[1+D[k1[x], x]^2], {x, Sqrt[3]/2-1, 0}] + 2*Pi*Integrate[k2[x]*Sqrt[1+D[k2[x], x]^2], {x, 0, Sqrt[3]/2}]
RealDigits[2*Pi - Pi^2/3, 10, 120][[1]] (* Amiram Eldar, May 22 2023 *)

Crossrefs

Cf. A102888, A137615, A137616, A137617.

Sequence in context: A201894 A023400 A153637 * A340866 A021338 A021889

Adjacent sequences: A137615 A137616 A137617 * A137619 A137620 A137621

Keyword

cons,easy,nonn

Author

Christof Weber, Feb 04 2008

Status

approved