A380004 Decimal expansion of obtuse vertex angles, in radians, in a pentagonal hexecontahedron face.

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

Offset: 1

Author

Paolo Xausa, Jan 12 2025

Keywords

• nonn
• cons
• easy

Comments

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (A380003) and four (equal) obtuse angles (this constant).

Examples

			2.06187303432440735586609817608931599292105069088...
		

Links

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

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380003 (face acute angle).

Programs

Mathematica

First[RealDigits[ArcCos[Root[64*#^6 - 128*#^5 + 64*#^4 + 24*#^3 - 24*#^2 + 1 &, 1]], 10, 100]]

Formula

Equals arccos(c), where c is the smallest real root of 64*x^6 - 128*x^5 + 64*x^4 + 24*x^3 - 24*x^2 + 1.

Equals (3*Pi - A380003)/4.