A380776 Decimal expansion of the acute vertex angle, in radians, in a pentagonal icositetrahedron face.

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

Offset

1,2

Comments

A pentagonal icositetrahedron face is an irregular pentagon with one acute angle (this constant) and four (equal) obtuse angles (A380777).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pentagonal Icositetrahedron.

Wikipedia, Pentagonal icositetrahedron.

Formula

Equals arccos(2 - A058265).

Equals arccos(c), where c is the real root of x^3 - 5*x^2 + 7*x - 1.

Equals 3*Pi - 4*A380777.

Example

1.409383078032028992695156056940530514142047762023...

Mathematica

First[RealDigits[ArcCos[Root[#^3 - 5*#^2 + 7*# - 1 &, 1]], 10, 100]]

Crossrefs

Cf. A058265, A378823, A378824, A378825, A378826, A378827, A380775, A380777.

Sequence in context: A390750 A133844 A198238 * A344716 A187377 A187155

Adjacent sequences: A380773 A380774 A380775 * A380777 A380778 A380779

Keyword

nonn,cons,easy

Author

Paolo Xausa, Feb 03 2025

Status

approved