

A137618


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


3



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
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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. 4355.


LINKS



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]/21, 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



KEYWORD



AUTHOR



STATUS

approved



