A384473 Decimal expansion of the middle interior angle (in degrees) in Albrecht Dürer's approximate construction of the regular pentagon.

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

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.

Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 181-182.

Links

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

Alexander Bogomolny, Approximate Construction of Regular Pentagon by A. Dürer.

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

Wikipedia, Albrecht Dürer.

Formula

Equals 135 - 180*arcsin(sqrt(3)*sin(Pi/12))/Pi.

Equals (Pi + arctan((3 - sqrt(3) + sqrt(6*sqrt(3) - 4))/(3 - sqrt(3) - sqrt(6*sqrt(3) - 4))))*180/Pi.

Equals (540 - 2*A384475 - A384477)/2.

A384475 < this constant < A384477.

Example

108.366120162561467008046935277164429896133431...

Mathematica

RealDigits[(3Pi/4-ArcSin[Sqrt[3]Sin[Pi/12]])180/Pi, 10, 100][[1]] (* or *)
RealDigits[(Pi+ArcTan[(3-Sqrt[3]+Sqrt[6Sqrt[3]-4])/(3-Sqrt[3]-Sqrt[6Sqrt[3]-4])])180/Pi, 10, 100][[1]]

Crossrefs

Cf. A228719, A384474 (in radians).

Cf. A002194, A019824, A072097, A177870.

Cf. A384475, A384476, A384477, A384478.

Sequence in context: A304583 A104697 A228211 * A010522 A388371 A197332

Adjacent sequences: A384470 A384471 A384472 * A384474 A384475 A384476

Keyword

nonn,cons

Author

Stefano Spezia, May 30 2025

Status

approved