A380940 -id:A380940

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A380941

Decimal expansion of the middle vertex angle, in radians, in a disdyakis triacontahedron face.

+10
5

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

A disdyakis triacontahedron face is a scalene triangle with three acute angles.

LINKS

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

Wikipedia, Disdyakis triacontahedron.

FORMULA

Equals arccos((17 - 4*A001622)/20).

Equals Pi - A380940 - A380942.

EXAMPLE

1.016443446896330150160097551517069643637928892906...

MATHEMATICA

First[RealDigits[ArcCos[(17 - 4*GoldenRatio)/20], 10, 100]]

CROSSREFS

Cf. A380940 (smallest face angle), A380942 (largest face angle).

Cf. A001622, A379388, A379708, A379709, A379710, A379711.

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Feb 08 2025

STATUS

approved

A380942

Decimal expansion of the largest vertex angle, in radians, in a disdyakis triacontahedron face.

+10
5

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A disdyakis triacontahedron face is a scalene triangle with three acute angles.

LINKS

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

Wikipedia, Disdyakis triacontahedron.

FORMULA

Equals arccos((7 - 4*A001622)/30).

Equals Pi - A380940 - A380941.

EXAMPLE

1.5531999505740762323183912046070949990519364517956...

MATHEMATICA

First[RealDigits[ArcCos[(7 - 4*GoldenRatio)/30], 10, 100]]

CROSSREFS

Cf. A380940 (smallest face angle), A380941 (middle face angle).

Cf. A001622, A379388, A379708, A379709, A379710, A379711.

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Feb 09 2025

STATUS

approved

A380981

Decimal expansion of the medium/short edge length ratio of a disdyakis triacontahedron.

+10
2

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.

Wikipedia, Disdyakis triacontahedron.

FORMULA

Equals (3/10)*(3 + sqrt(5)) = (3/10)*(3 + A002163).

Equals A176015 + 2/5.

EXAMPLE

1.57082039324993690892275210061938287063218550788...

MATHEMATICA

First[RealDigits[3/10*(3 + Sqrt[5]), 10, 100]]

CROSSREFS

Cf. A380982 (long/short edge length ratio).

Cf. A002163, A379388, A379708, A379709, A379710, A379711, A380940, A380941, A380942.

Apart from leading digits the same as A176015, A134976 and A010499.

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Feb 10 2025

STATUS

approved

A380982

Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.

+10
2

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.

Wikipedia, Disdyakis triacontahedron.

FORMULA

Equals 1/sqrt(5) + 7/5 = A020762 + 7/5.

EXAMPLE

1.8472135954999579392818347337462552470881236719223...

MATHEMATICA

First[RealDigits[7/5 + 1/Sqrt[5], 10, 100]] (* Paolo Xausa, Feb 10 2025 *)

CROSSREFS

Cf. A380981 (medium/short edge length ratio).

Cf. A020762, A379388, A379708, A379709, A379710, A379711, A380940, A380941, A380942.

Apart from leading digits the same as A176453, A134974 and A010476.

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Feb 10 2025

STATUS

approved

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