A396662 Decimal expansion of (745 + 262*sqrt(5))/18000.

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

Offset

0,2

Comments

The mean area of a triangle formed by independently and uniformly selecting at random three points in the interior of a unit-area regular 10-gon.

References

H. A. Alikoski, Über das Sylvestersche Vierpunktproblem, Ann. Acad. Sci. Fenn., Vol. 51, No. 7 (1939), pp. 1-10.

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Mean Triangle Area.

Eric Weisstein's World of Mathematics, Polygon Triangle Picking.

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 64800000*x^2 - 5364000*x + 42361.

Example

0.07393610056138582780328908340042190964919122278990109...

Mathematica

RealDigits[(745 + 262*Sqrt[5])/18000, 10, 120, -1][[1]]

Prog

(PARI) (745 + 262*sqrt(5))/18000

Crossrefs

Cf. A093582 (circle), A093587 (disk), A394834 (quadrant), A394835 (half-disk), A396660 (regular pentagon), A396661 (regular octagon), this constant (regular 10-gon), A396663 (ball).

Sequence in context: A361604 A003957 A021579 * A388163 A139788 A093525

Adjacent sequences: A396655 A396660 A396661 * A396663 A396664 A396665

Keyword

nonn,cons,new

Author

Amiram Eldar, Jun 02 2026

Status

approved