A380003 Decimal expansion of acute vertex angle, in radians, in a pentagonal hexecontahedron face.

1, 1, 7, 7, 2, 8, 5, 8, 2, 3, 4, 7, 1, 7, 5, 0, 2, 9, 1, 9, 2, 3, 5, 3, 7, 4, 4, 5, 4, 8, 1, 2, 4, 4, 6, 8, 0, 9, 0, 7, 3, 0, 5, 4, 3, 4, 5, 9, 8, 1, 2, 4, 8, 7, 4, 3, 0, 8, 9, 3, 3, 3, 8, 2, 9, 2, 3, 3, 2, 2, 9, 9, 7, 6, 3, 0, 9, 5, 9, 8, 0, 6, 4, 5, 2, 5, 2, 9, 6, 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 (this constant) and four (equal) obtuse angles (A380004).

Examples

			1.1772858234717502919235374454812446809073054345981...
		

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), A380004 (face obtuse angles).

Programs

Mathematica

First[RealDigits[ArcCos[Root[64*#^6 - 384*#^5 + 384*#^4 + 888*#^3 + 168*#^2 - 128*# - 31 &, 4]], 10, 100]]

Formula

Equals arccos(c), where c is the largest real root of 64*x^6 - 384*x^5 + 384*x^4 + 888*x^3 + 168*x^2 - 128*x - 31.

Equals 3*Pi - 4*A380004.