A380777 Decimal expansion of the obtuse vertex angles, in radians, in a pentagonal icositetrahedron face.

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

Offset: 1

Author

Paolo Xausa, Feb 03 2025

Keywords

• nonn
• cons
• easy

Comments

A pentagonal icositetrahedron face is an irregular pentagon with one acute angle (A380776) and four (equal) obtuse angles (this constant).

Examples

			2.0038487206843376806731935232244945346123651090255...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentagonal Icositetrahedron.
• Wikipedia, Pentagonal icositetrahedron.

Crossrefs

Cf. A058265, A378823, A378824, A378825, A378826, A378827, A380775, A380776.

Programs

Mathematica

First[RealDigits[ArcCos[Root[4*#^3 - 4*#^2 + 1 &, 1]], 10, 100]]

Formula

Equals arccos((1 - A058265)/2).

Equals arccos(c), where c is the real root of 4*x^3 - 4*x^2 + 1.

Equals (3*Pi - A380776)/4.