A384477 Decimal expansion of the largest interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

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

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.

Wikipedia, Albrecht Dürer.

Formula

Equals 540 - 2*(A384473 + A384475).

Equals (90*(Pi + 4*arccsc(2/sqrt(2 - sqrt(2*(5 - 2*sqrt(3) + sqrt(-187 + 108*sqrt(3))))))))/Pi.

Example

109.19210783168876707355415731659880064894477011...

Mathematica

RealDigits[(90 (Pi + 4 ArcCsc[2/Sqrt[2 - Sqrt[2 (5 - 2 Sqrt[3] + Sqrt[-187 + 108 Sqrt[3]])]]]))/Pi, 10, 100][[1]]

Crossrefs

Cf. A228719, A384478 (in radians).

Cf. A384473, A384474, A384475, A384476.

Sequence in context: A339354 A280375 A067617 * A230458 A246687 A021525

Adjacent sequences: A384474 A384475 A384476 * A384478 A384479 A384480

Keyword

nonn,cons

Author

Stefano Spezia, May 30 2025

Status

approved