A376642 Decimal expansion of the area of Moss's egg constructed from a unit-hypotenuse right isosceles triangle.

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

Offset

0,1

Comments

Moss's egg is an oval named by Dixon (1987) after Stephanie Moss. It is formed by four circular arcs. The shape is composed of the area of a half disk of radius 1/2, circular sector with radius 1-sqrt(2)/2 and central angle Pi/2, and two partially overlapping circular sectors with radius 1 and central angle Pi/4, whose common area is of the unit-hypotenuse right isosceles triangle.

The perimeter of the shape is (3-sqrt(2)/2)*Pi/2.

References

Robert Dixon, Mathographics, New York: Dover, 1987. See p. 5.

Anna Weltman, Not Your Average Maths Book, Wide Eyed Editions, 2022. See p. 43.

Links

Table of n, a(n) for n=0..104.

Michael Borcherds and Bill Lombard, Moss Egg by Robert Dixon, GeoGebra.

Eric Weisstein's World of Mathematics, Moss's Egg.

Wikipedia, Moss's egg.

Formula

Equals ((3-sqrt(2))*Pi - 1)/4.

Example

0.99547375565275336709301228994445373849422162718740...

Mathematica

RealDigits[((3 - Sqrt[2])*Pi - 1)/4, 10, 120][[1]]

Prog

(PARI) ((3-quadgen(8))*Pi - 1)/4

Crossrefs

Similar constants: A093731, A259830, A336266, A336308.

Sequence in context: A155995 A347151 A229191 * A347166 A347081 A347152

Adjacent sequences: A376639 A376640 A376641 * A376643 A376644 A376645

Keyword

nonn,cons

Author

Amiram Eldar, Sep 30 2024

Status

approved