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A376642
Decimal expansion of the area of Moss's egg constructed from a unit-hypotenuse right isosceles triangle.
0
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
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
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Sep 30 2024
STATUS
approved