A395729 Decimal expansion of the ratio of the minimum area to the mean area of the orthogonal projection of a regular icosahedron.

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

Offset

0,1

Comments

See A395727 for more details.

References

G. Kallianpur, P. R. Krishnaiah, and J. K. Ghosh, Statistics and Probability: Essays in Honor of C. R. Rao, North-Holland Pub. Co., New York, 1982, p. 514.

Luis A. Santaló, Integral Geometry and Geometric Probability, 2nd ed., Cambridge University Press, 2004, p. 218.

Links

Table of n, a(n) for n=0..104.

U. Betke and P. McMullen, Estimating the sizes of convex bodies from projections, Journal of the London Mathematical Society, Vol. s2-27, No. 3 (1983), pp. 525-538.

M. G. Kendall and P. A. P. Moran, Geometrical Probability, Charles Griffin & Co., London, 1962, p. 74.

P. A. P. Moran, Measuring the Surface Area of a Convex Body, Annals of Mathematics, Vol. 45, No. 4 (1944), pp. 793-799.

Index entries for algebraic numbers, degree 04.

Index entries for sequences related to icosahedron.

Formula

Equals sqrt(2/15) * phi^2, where phi is the golden ratio (A001622).

Equals A388812 / A245294.

Minimal polynomial: 225*x^4 - 210*x^2 + 4.

Example

0.955970847969029129823183795251784032613735941774094...

Mathematica

RealDigits[Sqrt[2/15] * GoldenRatio^2, 10, 120][[1]]

Prog

(PARI) sqrt(2/15) * quadgen(5)^2

Crossrefs

Cf. A001622, A245294, A388812, A395727, A395728.

Sequence in context: A200026 A262276 A244844 * A390072 A392510 A255896

Adjacent sequences: A395726 A395727 A395728 * A395730 A395731 A395732

Keyword

nonn,cons

Author

Amiram Eldar, May 05 2026

Status

approved