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, 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

Author

Amiram Eldar, Jun 23 2022

Keywords

• nonn
• cons

Comments

The shape is formed by the intersection of four parabolas. Its area is given in A355183.

Examples

			1.70308249665895322783584912274920315719803442295049...
		

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.

Crossrefs

Cf. A103712, A244921, A254140, A352453, A355183 (area).

Programs

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]]

Formula

Equals 2*log(sqrt(4-2*sqrt(2))+sqrt(2)-1) - sqrt(16-8*sqrt(2)) + sqrt(32-16*sqrt(2)).