A384478 Decimal expansion of the largest interior angle (in radians) in Albrecht Dürer's approximate construction of the regular pentagon.

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

Offset: 1

Author

Stefano Spezia, May 30 2025

Keywords

• nonn
• cons

Examples

			1.9057617988556553228528885242146948475110453569...
		

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.
• Wikipedia, Albrecht Dürer.

Crossrefs

Cf. A228719, A384477 (in degrees).

Cf. A384473, A384474, A384475, A384476.

Programs

Mathematica

RealDigits[((Pi + 4 ArcCsc[2/Sqrt[2 - Sqrt[2 (5 - 2 Sqrt[3] + Sqrt[-187 + 108 Sqrt[3]])]]]))/2,10,100][[1]]

Formula

Equals 3*Pi - 2*(A384474 + A384476).

Equals ((Pi + 4*arccsc(2/sqrt(2 - sqrt(2*(5 - 2*sqrt(3) + sqrt(-187 + 108*sqrt(3))))))))/2.