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A355184
Decimal expansion of the perimeter of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.
1
1, 7, 0, 3, 0, 8, 2, 4, 9, 6, 6, 5, 8, 9, 5, 3, 2, 2, 7, 8, 3, 5, 8, 4, 9, 1, 2, 2, 7, 4, 9, 2, 0, 3, 1, 5, 7, 1, 9, 8, 0, 3, 4, 4, 2, 2, 9, 5, 0, 4, 9, 7, 7, 1, 2, 1, 2, 1, 6, 6, 0, 3, 7, 8, 4, 2, 1, 7, 2, 6, 9, 2, 4, 5, 5, 2, 3, 3, 5, 0, 4, 9, 0, 3, 5, 1, 6, 3, 3, 3, 3, 1, 2, 3, 5, 3, 4, 0, 2, 3, 8, 9, 5, 7, 0
OFFSET
1,2
COMMENTS
The shape is formed by the intersection of four parabolas. Its area is given in A355183.
LINKS
Amiram Eldar, Illustration.
Missouri State University, Problem #5, The Area and Perimeter of a Certain Region, Advanced Problem Archive; Solution to Problem #5, by John Shonder.
FORMULA
Equals 2*log(sqrt(4-2*sqrt(2))+sqrt(2)-1) - sqrt(16-8*sqrt(2)) + sqrt(32-16*sqrt(2)).
EXAMPLE
1.70308249665895322783584912274920315719803442295049...
MATHEMATICA
RealDigits[2*Log[Sqrt[4 - 2*Sqrt[2]] + Sqrt[2] - 1] - Sqrt[16 - 8*Sqrt[2]] + Sqrt[32 - 16*Sqrt[2]], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 23 2022
STATUS
approved