A240969 -id:A240969 - cp's OEIS frontend

A379390 Decimal expansion of 1/A240969.

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

Offset: 1

Stefano Spezia, Dec 22 2024

			2.2782916414404375436614925707174763091505974327...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4.1, p. 493.

Cf. A240969.

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); RealDigits[1/beta, 10, 100] // First (* after Jean-François Alcover, Sep 04 2014 in A240969 *)

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.

Original entry on oeis.org

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

Jean-François Alcover, Sep 19 2014

			0.39438476883681362825403921854319968160795399...

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

Cf. A240969 (beta).

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

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

A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Mar 26 2015

A cubic number of denominator 3 and minimal polynomial 3x^6 + 36x^4 + 16x^2 - 64. - Charles R Greathouse IV, May 13 2019

			1.0435901095949847538118417712870227333548896969340378971...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, pp. 493-494.

J.-F. Alcover, Figure 8.3 A caliper. [after Steven Finch]
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 63.
Steven R. Finch and John E. Wetzel, Lost in a Forest
Index entries for algebraic numbers, degree 3

Cf. A240969, A244046.

RealDigits[Root[3*x^6 + 36*x^4 + 16*x^2 - 64, x, 2], 10, 103] // First

polrootsreal(3*x^6 + 36*x^4 + 16*x^2 - 64)[2] \\ Charles R Greathouse IV, May 13 2019

Sec(phi) = 1/sqrt(1 - (1/6 + (4/3)*sin((1/3)*arcsin(17/64)))^2), which is the positive root of 3*x^6 + 36*x^4 + 16*x^2 - 64.

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A379390 Decimal expansion of 1/A240969.

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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.

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A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.

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