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

Author

Stefano Spezia, May 30 2025

Keywords

• nonn
• cons

Examples

			107.03782592159414945517598606453616977939418394...
		

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

• Stefano Spezia, Albrecht Dürer's approximate construction of the regular pentagon.
• Stefano Spezia, Exact form of the constant.
• Wikipedia, Albrecht Dürer.

Crossrefs

Cf. A228719, A384476 (in radians).

Cf. A384474, A384476, A384477, A384478.

Programs

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]]

Formula

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