A380775 -id:A380775 - cp's OEIS frontend

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

Paolo Xausa, Feb 03 2025

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

			1.409383078032028992695156056940530514142047762023...

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

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

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

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.

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

Original entry on oeis.org

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

Paolo Xausa, Feb 03 2025

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

			2.0038487206843376806731935232244945346123651090255...

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

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

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

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.

cp's OEIS Frontend

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

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