{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T12:18:20Z","timestamp":1759666700409},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540422327"},{"type":"electronic","value":"9783540455455"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001]]},"DOI":"10.1007\/3-540-45545-0_84","type":"book-chapter","created":{"date-parts":[[2007,11,16]],"date-time":"2007-11-16T14:01:49Z","timestamp":1195221709000},"page":"728-737","source":"Crossref","is-referenced-by-count":3,"title":["Apollonius Tenth Problem as a Point Location Problem"],"prefix":"10.1007","author":[{"given":"Deok-Soo","family":"Kim","sequence":"first","affiliation":[]},{"given":"Donguk","family":"Kim","sequence":"additional","affiliation":[]},{"given":"Kokichi","family":"Sugihara","sequence":"additional","affiliation":[]},{"given":"Joonghyun","family":"Ryu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2001,7,17]]},"reference":[{"key":"84_CR1","first-page":"173","volume-title":"College Geometry","author":"N. Altshiller-Court","year":"1952","unstructured":"Altshiller-Court, N., The problem of Apollonius. College Geometry, 2nd Ed., Barnes and Noble, New York, (1952) 173\u2013181.","edition":"2nd Ed."},{"key":"84_CR2","volume-title":"A History of Mathematics","author":"C. B. Boyer","year":"1968","unstructured":"Boyer, C. B., A History of Mathematics, Wiley, New York (1968)."},{"key":"84_CR3","unstructured":"Capelli, R. Circle tangential to 3 cicles or lines. Posting No. 35067, Usenet newsgroup comp.graphics.algorithms, 2 pages, (1996)."},{"key":"84_CR4","volume-title":"An Elementary Approach to Ideas and Methods","author":"R. Courant","year":"1996","unstructured":"Courant, R. and Robbins, H., What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd edition, Oxford University Press, Oxford (1996).","edition":"2nd edition"},{"key":"84_CR5","volume-title":"100 Great Problems of Elementary Mathematics: Their History and Solutions","author":"H. D\u00f6rrie","year":"1965","unstructured":"D\u00f6rrie, H., 100 Great Problems of Elementary Mathematics: Their History and Solutions, Dover, New York (1965)."},{"key":"84_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/S0167-8396(98)00039-9","volume":"16","author":"M. Gavrilova","year":"1999","unstructured":"Gavrilova, M. and Rokne, J., Swap conditions for dynamic Voronoi diagram for circles and line segments, Computer Aided Geometric Design, Vol. 16 (1999) 89\u2013106.","journal-title":"Computer Aided Geometric Design"},{"key":"84_CR7","unstructured":"Gavrilova, M. and Rokne, J., Apollonius\u2019 Tenth Problem Revisited, Special Session on Recent Progress in Elementary Geometry, 941st American Mathematical Society Conference (1999) 64."},{"issue":"8","key":"84_CR8","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1016\/0010-4485(95)99797-C","volume":"27","author":"D.-S. Kim","year":"1995","unstructured":"Kim, D.-S., Hwang, I.-K. and Park, B.-J., Representing the Voronoi diagram of a simple polygon using rational quadratic B\u00e9zier curves, Computer-Aided Design, Vol. 27, No. 8 (1995) 605\u2013614.","journal-title":"Computer-Aided Design"},{"issue":"13","key":"84_CR9","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1016\/S0010-4485(98)00052-9","volume":"30","author":"D.-S. Kim","year":"1998","unstructured":"Kim, D.-S., Lee, S.-W. and Shin, H., A cocktail algorithm for planar B\u00e9zier curve intersections, Computer-Aided Design, Vol. 30, No. 13 (1998) 1047\u20131051.","journal-title":"Computer-Aided Design"},{"key":"84_CR10","doi-asserted-by":"crossref","unstructured":"Kim, D.-S., Kim, D. and Sugihara, K., Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology, (Submitted to Computer Aided Geometric Design 2001).","DOI":"10.1007\/3-540-40996-3_37"},{"key":"84_CR11","doi-asserted-by":"crossref","unstructured":"Kim, D.-S., Kim, D. and Sugihara, K., Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry, (Submitted to Computer Aided Geometric Design 2001).","DOI":"10.1007\/3-540-40996-3_37"},{"key":"84_CR12","unstructured":"Kreyszig, E., Advanced Engineering Mathematics, 7th Edition, John Wiley & Sons (1993)."},{"issue":"1","key":"84_CR13","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1137\/0210006","volume":"10","author":"D. T. Lee","year":"1981","unstructured":"Lee, D. T. and Drysdale, R. L., III, Generalization of Voronoi diagrams in the plane, SIAM J. COMPUT., Vol. 10, No. 1 (1981) 73\u201387.","journal-title":"SIAM J. COMPUT."},{"key":"84_CR14","volume-title":"Elementary Geometry from an Advanced Standpoint","author":"E. E. Moise","year":"1990","unstructured":"Moise, E. E., Elementary Geometry from an Advanced Standpoint, 3rd. ed., Addison-Wesley Publ. Co., Reading (1990).","edition":"3rd. ed."},{"key":"84_CR15","unstructured":"Okabe, A., Boots, B. and Sugihara, K., Spatial Tessellations Concepts and Applications of Voronoi Diagram, John Wiley & Sons (1992)."},{"key":"84_CR16","doi-asserted-by":"crossref","unstructured":"Rokne, J., Appolonius\u2019s 10th problem, Graphics Gems II, ed. James Arvo, Academic Press, (1991) 19\u201324.","DOI":"10.1016\/B978-0-08-050754-5.50016-5"},{"key":"84_CR17","first-page":"203","volume-title":"Graphics Gems","author":"C. A. Sevici","year":"1992","unstructured":"Sevici, C. A., Solving the problem of Apollonius and other related problems, Graphics Gems III, ed. David Kirk, Academic Press, San Diego (1992) 203\u2013209."},{"issue":"2","key":"84_CR18","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1137\/0214034","volume":"14","author":"M. Sharir","year":"1985","unstructured":"Sharir, M., Intersection and closest-pair problems for a set of planar discs, SIAM J. COMPUT., Vol. 14, No. 2 (1985) 448\u2013468.","journal-title":"SIAM J. COMPUT."}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2014 ICCS 2001"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45545-0_84","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,4]],"date-time":"2019-05-04T11:37:21Z","timestamp":1556969841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45545-0_84"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783540422327","9783540455455"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/3-540-45545-0_84","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2001]]}}}