A395729 - OEIS

%I #4 May 06 2026 00:55:45

%S 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,

%T 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,

%U 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

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

%C See A395727 for more details.

%D 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.

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

%H U. Betke and P. McMullen, <a href="https://doi.org/10.1112/jlms/s2-27.3.525">Estimating the sizes of convex bodies from projections</a>, Journal of the London Mathematical Society, Vol. s2-27, No. 3 (1983), pp. 525-538.

%H M. G. Kendall and P. A. P. Moran, <a href="https://archive.org/details/geometricalproba033077mbp/page/n77/mode/1up">Geometrical Probability</a>, Charles Griffin & Co., London, 1962, p. 74.

%H P. A. P. Moran, <a href="https://www.jstor.org/stable/1969305">Measuring the Surface Area of a Convex Body</a>, Annals of Mathematics, Vol. 45, No. 4 (1944), pp. 793-799.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 04</a>.

%H <a href="/index/Ia#icosahedron">Index entries for sequences related to icosahedron</a>.

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

%F Equals A388812 / A245294.

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

%e 0.955970847969029129823183795251784032613735941774094...

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

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 05 2026