proposed

approved

editing

proposed

Missouri State University, <a href="http://people.missouristate.edu/lesreid/Adv05.html">Problem #5, The Area and Perimeter of a Certain Region</a>, Advanced Problem Archive; <a href="http://people.missouristate.edu/lesreid/Adv05AdvSol05.html">Solution to Problem #5</a>, by John Shonder.

allocated for Amiram EldarDecimal 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

1,2

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

Amiram Eldar, <a href="/A355183/a355183.jpg">Illustration</a>.

Missouri State University, <a href="http://people.missouristate.edu/lesreid/Adv05.html">Problem #5, The Area and Perimeter of a Certain Region</a>, Advanced Problem Archive; <a href="http://people.missouristate.edu/lesreid/Adv05.html">Solution to Problem #5</a>, by John Shonder.

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

1.70308249665895322783584912274920315719803442295049...

RealDigits[2*Log[Sqrt[4 - 2*Sqrt[2]] + Sqrt[2] - 1] - Sqrt[16 - 8*Sqrt[2]] + Sqrt[32 - 16*Sqrt[2]], 10, 100][[1]]

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

allocated

nonn,cons

Amiram Eldar, Jun 23 2022

approved

editing

allocated for Amiram Eldar

allocated

approved