{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T01:31:01Z","timestamp":1778808661769,"version":"3.51.4"},"reference-count":18,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1998,2,1]],"date-time":"1998-02-01T00:00:00Z","timestamp":886291200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5645,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1998,2]]},"DOI":"10.1016\/s0012-365x(97)00050-2","type":"journal-article","created":{"date-parts":[[2003,4,23]],"date-time":"2003-04-23T20:16:34Z","timestamp":1051128994000},"page":"139-154","source":"Crossref","is-referenced-by-count":179,"title":["Dense packings of congruent circles in a circle"],"prefix":"10.1016","volume":"181","author":[{"given":"R.L.","family":"Graham","sequence":"first","affiliation":[]},{"given":"B.D.","family":"Lubachevsky","sequence":"additional","affiliation":[]},{"given":"K.J.","family":"Nurmela","sequence":"additional","affiliation":[]},{"given":"P.R.J.","family":"\u00d6sterg\u00e5rd","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0012-365X(97)00050-2_BIB1","first-page":"329","article-title":"The closest packing of equal circles on a sphere","volume":"405","author":"Clare","year":"1986"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB2","series-title":"Sphere Packings, Lattices and Groups","author":"Conway","year":"1993"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB3","series-title":"Unsolved Problems in Geometry","author":"Croft","year":"1991"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB4","series-title":"Lagerungen in der Ebene, auf der Kugel und im Raum","author":"Fejes T\u00f3th","year":"1972"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB5","doi-asserted-by":"crossref","first-page":"134","DOI":"10.2307\/2688222","article-title":"Packing of 14, 16, 17 and 20 circles in a circle","volume":"44","author":"Goldberg","year":"1971","journal-title":"Math. Mag."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB6","first-page":"192","article-title":"Sets of points with given minimum separation (Solution to Problem E1921)","volume":"75","author":"Graham","year":"1968","journal-title":"Amer. Math. Monthly"},{"issue":"A1","key":"10.1016\/S0012-365X(97)00050-2_BIB7","first-page":"39","article-title":"Dense packings of equal disks in an equilateral triangle: from 22 to 34 and beyond","volume":"2","author":"Graham","year":"1995","journal-title":"Electron. J. Combin."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02187775","article-title":"Penny-packing and two-dimensional codes","volume":"5","author":"Graham","year":"1990","journal-title":"Discrete Comput. Geom."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB9","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1145\/78928.78931","article-title":"Algorithm 681: INTBIS, a portable interval Newton\/bisection package","volume":"16","author":"Kearfott","year":"1990","journal-title":"ACM Trans. Math. Software"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2307\/2688509","article-title":"Packing cylinders into cylindrical containers","volume":"40","author":"Kravitz","year":"1967","journal-title":"Math. Mag."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB11","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0021-9991(91)90222-7","article-title":"How to simulate billiards and similar systems","volume":"94","author":"Lubachevsky","year":"1991","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB12","doi-asserted-by":"crossref","unstructured":"B.D. Lubachevsky, R.L. Graham, Curved hexagonal packings of equal disks in a circle, Discrete Comput. Geom., to appear.","DOI":"10.1007\/PL00009314"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB13","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01263647","article-title":"Densest packing of eleven congruent circles in a circle","volume":"50","author":"Melissen","year":"1994","journal-title":"Geom. Dedicata"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB14","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0012-365X(95)90139-C","article-title":"Packing 16, 17 or 18 circles in an equilateral triangle","volume":"145","author":"Melissen","year":"1995","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB15","article-title":"Constructing spherical codes by global optimization methods","author":"Nurmela","year":"1995"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB16","doi-asserted-by":"crossref","unstructured":"K.J. Nurmela, P.R.J. \u00d6sterg\u00e1rd, Packing up to 50 equal circles in a square, Discrete Comput. Geom., to appear.","DOI":"10.1007\/PL00009306"},{"key":"10.1016\/S0012-365X(97)00050-2_BIB17","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/mana.19690400110","article-title":"Der Mindestabstand von n in der Einbeitskreisscheibe gelegenen Punkten","volume":"40","author":"Pirl","year":"1969","journal-title":"Math. Nachr."},{"key":"10.1016\/S0012-365X(97)00050-2_BIB18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/2689291","article-title":"Dense packing of equal circles within a circle","volume":"48","author":"Reis","year":"1975","journal-title":"Math. Mag."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X97000502?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X97000502?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T18:51:44Z","timestamp":1556131904000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X97000502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2]]},"references-count":18,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1998,2]]}},"alternative-id":["S0012365X97000502"],"URL":"https:\/\/doi.org\/10.1016\/s0012-365x(97)00050-2","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1998,2]]}}}