article published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Nany Hasan author Raimund Seidel author Xiao Shen author This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n12−112+O(1)n47 points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k. Springer1989 eng 0046-5755 1572-916810.1007/BF00181432 3211 - 12 yes Edelsbrunner H, Hasan N, Seidel R, Shen X. Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. 1989;32(1):1-12. doi:<a href="https://doi.org/10.1007/BF00181432">10.1007/BF00181432</a> Edelsbrunner H, Hasan N, Seidel R, Shen X. 1989. Circles through two points that always enclose many points. Geometriae Dedicata. 32(1), 1–12. H. Edelsbrunner, N. Hasan, R. Seidel, X. Shen, Geometriae Dedicata 32 (1989) 1–12. H. Edelsbrunner, N. Hasan, R. Seidel, and X. Shen, “Circles through two points that always enclose many points,” <i>Geometriae Dedicata</i>, vol. 32, no. 1. Springer, pp. 1–12, 1989. Edelsbrunner, Herbert, et al. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>, vol. 32, no. 1, Springer, 1989, pp. 1–12, doi:<a href="https://doi.org/10.1007/BF00181432">10.1007/BF00181432</a>. Edelsbrunner, H., Hasan, N., Seidel, R., &#38; Shen, X. (1989). Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. Springer. <a href="https://doi.org/10.1007/BF00181432">https://doi.org/10.1007/BF00181432</a> Edelsbrunner, Herbert, Nany Hasan, Raimund Seidel, and Xiao Shen. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>. Springer, 1989. <a href="https://doi.org/10.1007/BF00181432">https://doi.org/10.1007/BF00181432</a>. 40802018-12-11T12:06:49Z2022-02-14T09:55:28Z