A343143 Decimal expansion of the angle in radians at the apex of the Calabi triangle.

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

Offset

1,2

Comments

The angle in degrees is 101.7359477153... and each of the base angles is 0.6829826991... radians or 39.1320261423... degrees.

References

John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus (Springer-Verlag), 1996, p. 206.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 8.13, pp. 523-524.

Links

Table of n, a(n) for n=1..87.

Eugenio Calabi, Outline of Proof Regarding Squares Wedged in Triangle, 1997.

Eric Weisstein's World of Mathematics, Calabi's Triangle.

Wikipedia, Calabi triangle.

Formula

Equals 2*arcsin(c/2), where c = A046095.

Example

1.77562725526962986250848167202872854269509176556866...

Mathematica

r = x /. FindRoot[2 x^3 - 2 x^2 - 3 x + 2 == 0, {x, 1.5}, WorkingPrecision -> 200]; RealDigits[2*ArcSin[r/2], 10, 100][[1]]

Crossrefs

Cf. A046095.

Sequence in context: A336078 A074917 A154016 * A220781 A198566 A154193

Adjacent sequences: A343140 A343141 A343142 * A343144 A343145 A343146

Keyword

nonn,cons

Author

Amiram Eldar, Jun 18 2021

Status

approved