A384475 Decimal expansion of the smallest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

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

Offset

3,3

References

Alfred S. Posamentier and Herbert A. Hauptman, 101 great ideas for introducing key concepts in mathematics: a resource for secondary school teachers, Corwin Press, Inc., 2001. See pages 144-145.

Links

Table of n, a(n) for n=3..102.

Stefano Spezia, Albrecht Dürer's approximate construction of the regular pentagon.

Stefano Spezia, Exact form of the constant.

Wikipedia, Albrecht Dürer.

Formula

Equals (540 - 2*A384473 - A384477)/2.

Example

107.03782592159414945517598606453616977939418394...

Mathematica

RealDigits[180(1 + ArcTan[(-10 + 10 Sqrt[3] + 2 Sqrt[-4 + 6 Sqrt[3]] +2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] -3 Sqrt[2 (8 - 2 Sqrt[3] -Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])])/(2 + 2 Sqrt[3] + 2 Sqrt[6 (-2 + 3 Sqrt[3])] - 4 Sqrt[-4 + 6 Sqrt[3]] - 2 Sqrt[-34 + 28 Sqrt[3] + 5 Sqrt[6 (-2 + 3 Sqrt[3])] - 11 Sqrt[-4 + 6 Sqrt[3]]] - 3 Sqrt[2 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] + Sqrt[-4 + 6 Sqrt[3]])] + Sqrt[6 (8 - 2 Sqrt[3] - Sqrt[6 (-2 + 3 Sqrt[3])] +Sqrt[-4 + 6 Sqrt[3]])])]/Pi), 10, 100][[1]]

Crossrefs

Cf. A228719, A384476 (in radians).

Cf. A384474, A384476, A384477, A384478.

Sequence in context: A126583 A220359 A021591 * A396820 A316599 A077185

Adjacent sequences: A384472 A384473 A384474 * A384476 A384477 A384478

Keyword

nonn,cons

Author

Stefano Spezia, May 30 2025

Status

approved