A393430 Decimal expansion of the probability that the cusp of a given cardioid lies within the triangle formed by three points chosen uniformly and independently at random from the interior of that cardioid.

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

Offset

0,2

Links

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

Eugen J. Ionaşcu, Random triangles in planar regions, Rendiconti del Circolo Matematico di Palermo, Series 2, Vol. 68 (2019), pp. 363-383; arXiv preprint, arXiv:1612.08619 [math.HO], 2016-2018.

Eric Weisstein's World of Mathematics, Cardioid.

Wikipedia, Cardioid.

Index entries for transcendental numbers.

Formula

Equals 1/4 - 20/(9*Pi^2) (Ionaşcu, 2019, p. 375).

Example

0.0248418141281382856802678595339385802125360562838965...

Mathematica

RealDigits[1/4 - 20/(9*Pi^2), 10, 120, -1][[1]]

Prog

(PARI) 1/4 - 20/(9*Pi^2)

Crossrefs

Cf. A197723 (cardioid area).

Cf. A020773 (square or disk), A393427 (triangle), A393428 (pentagon), A393429 (disk with hole), this constant (cardioid).

Sequence in context: A344537 A349104 A059884 * A191561 A021805 A031401

Adjacent sequences: A393427 A393428 A393429 * A393431 A393432 A393433

Keyword

nonn,cons,easy

Author

Amiram Eldar, Feb 14 2026

Status

approved