A355183 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.

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, 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, 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

Offset

0,1

Comments

The shape is formed by the intersection of four parabolas. Its perimeter is given in A355184.

References

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.

Links

Table of n, a(n) for n=0..104.

Joel Atkins, Regular Polygon Targets, Pi Mu Epsilon Journal, Vol. 9, No. 3 (1989), pp. 142-144; entire issue.

Nicholas R. Baeth, Loren Luther, and Rhonda McKee, The Downtown Problem: Variations on a Putnam Problem, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.

John Coffey, Q19, Maths Puzzles & Problems, MathStudio, 2011.

Amiram Eldar, Illustration.

Leonard F. Klosinski, Gerald L. Alexanderson, and Loren C. Larson, The Fiftieth William Lowell Putnam Mathematical Competition, The American Mathematical Monthly, Vol. 98, No. 4 (1991), pp. 319-327.

Missouri State University, Problem #5, The Area and Perimeter of a Certain Region, Advanced Problem Archive; Solution to Problem #5, by John Shonder.

Jun-Ping Shi, Problem Set 9.

Formula

Equals (4*sqrt(2)-5)/3.

Example

0.21895141649746006506891829894626410475956250050259...

Mathematica

RealDigits[(4*Sqrt[2] - 5)/3, 10, 100][[1]]

Crossrefs

Cf. A021058, A103712, A244921, A254140, A352453, A355184 (perimeter), A355185 (3D analog).

Sequence in context: A075513 A284211 A246403 * A258502 A011019 A254979

Adjacent sequences: A355180 A355181 A355182 * A355184 A355185 A355186

Keyword

nonn,cons

Author

Amiram Eldar, Jun 23 2022

Status

approved