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%I #9 Jun 23 2022 13:49:07
%S 2,1,8,9,5,1,4,1,6,4,9,7,4,6,0,0,6,5,0,6,8,9,1,8,2,9,8,9,4,6,2,6,4,1,
%T 0,4,7,5,9,5,6,2,5,0,0,5,0,2,5,9,7,4,3,0,9,0,2,2,3,9,6,5,0,6,5,4,3,0,
%U 9,9,7,1,2,8,2,8,0,9,3,8,5,1,3,3,8,5,0,0,4,5,7,7,0,1,8,8,7,6,3,6,4,6,6,8,5
%N Decimal expansion of the area 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.
%C The shape is formed by the intersection of four parabolas. Its perimeter is given in A355184.
%D Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil, The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary, The Mathematical Association of America, 2002, pp. 108-109.
%H Joel Atkins, <a href="https://www.jstor.org/stable/24339911">Regular Polygon Targets</a>, Pi Mu Epsilon Journal, Vol. 9, No. 3 (1989), pp. 142-144; <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.9.No.3.pdf">entire issue</a>.
%H Nicholas R. Baeth, Loren Luther, and Rhonda McKee, <a href="http://www.jstor.org/stable/10.4169/math.mag.90.4.243">The Downtown Problem: Variations on a Putnam Problem</a>, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.
%H John Coffey, <a href="http://www.mathstudio.co.uk/problems.htm">Q19</a>, Maths Puzzles & Problems, MathStudio, 2011.
%H Amiram Eldar, <a href="/A355183/a355183.jpg">Illustration</a>.
%H Leonard F. Klosinski, Gerald L. Alexanderson, and Loren C. Larson, <a href="https://www.jstor.org/stable/2323799">The Fiftieth William Lowell Putnam Mathematical Competition</a>, The American Mathematical Monthly, Vol. 98, No. 4 (1991), pp. 319-327.
%H 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/AdvSol05.html">Solution to Problem #5</a>, by John Shonder.
%H Jun-Ping Shi, <a href="https://web.archive.org/web/20161130160803/http://www.math.wm.edu/~shij/putnam/answer-week-9.pdf">Problem Set 9</a>.
%F Equals (4*sqrt(2)-5)/3.
%e 0.21895141649746006506891829894626410475956250050259...
%t RealDigits[(4*Sqrt[2] - 5)/3, 10, 100][[1]]
%Y Cf. A021058, A103712, A244921, A254140, A352453, A355184 (perimeter), A355185 (3D analog).
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Jun 23 2022