A377698 Decimal expansion of 30*arcsin(sqrt(5)/3).

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

Offset

2,1

Comments

Dehn invariant of a regular icosahedron with unit edge length and (negated) of a truncated dodecahedron with unit edge length.

Links

Table of n, a(n) for n=2..91.

Brady Haran and Daniel Litt, The Dehn Invariant, Numberphile YouTube video, 2019.

Eric Weisstein's World of Mathematics, Dehn Invariant.

Eric Weisstein's World of Mathematics, Regular Icosahedron.

Eric Weisstein's World of Mathematics, Truncated Dodecahedron.

Wikipedia, Dehn Invariant.

Index entries for transcendental numbers

Formula

Equals 30*arccos(2/3) = 30*A228496.

Example

25.232060117037907673295750954792922401062363569...

Mathematica

First[RealDigits[30*ArcCos[2/3], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["Icosahedron", "DehnInvariant"], 10, 100]]

Prog

(PARI) 30*acos(2/3) \\ Charles R Greathouse IV, Nov 21 2024

Crossrefs

Cf. A228496.

Sequence in context: A100955 A049413 A300691 * A102707 A134486 A088006

Adjacent sequences: A377695 A377696 A377697 * A377699 A377700 A377701

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 05 2024

Status

approved