A247553 Decimal expansion of A(rectangles), an analog of Moser's worm constant, which is associated with the class of rectangular regions of the plane.

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

Offset: 0

Author

Jean-François Alcover, Sep 19 2014

Keywords

• nonn
• cons

Examples

			0.39438476883681362825403921854319968160795399...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 492.

Crossrefs

Cf. A240969 (beta).

Programs

Mathematica

phi = ArcSin[1/6 + (4/3)*Sin[(1/3)*ArcSin[17/64]]]; psi = ArcTan[(1/2)*Sec[phi]]; beta = (1/2)*(Pi/2 - phi - 2*psi + Tan[phi] + Tan[psi])^(-1); A = beta*Sqrt[1 - beta^2]; RealDigits[A, 10, 102] // First

Formula

A = beta*sqrt(1 - beta^2), where beta is A240969.