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

Author

Amiram Eldar, Sep 30 2024

Keywords

• nonn
• cons

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.

Examples

			0.99547375565275336709301228994445373849422162718740...
		

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

• Michael Borcherds and Bill Lombard, Moss Egg by Robert Dixon, GeoGebra.
• Eric Weisstein's World of Mathematics, Moss's Egg.
• Wikipedia, Moss's egg.

Crossrefs

Similar constants: A093731, A259830, A336266, A336308.

Programs

Mathematica

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

PARI

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

Formula

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