Nurmela, Kari J. Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles. (English) Zbl 0986.52011 Exp. Math. 9, No. 2, 241-250 (2000). Author’s abstract: This paper presents a computational method to find good, conjecturally optimal coverings of an equilateral triangle with equal circles. Best found coverings with up to 36 circles are displayed, 19 of which are either new or improve on earlier published coverings. Reviewer: Elena E.Berdysheva (Erlangen) Cited in 13 Documents MSC: 52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry) Keywords:covering; equilateral triangle × Cite Format Result Cite Review PDF Full Text: DOI Euclid EuDML References: [1] Ben-Israel A., J. Math. Anal. Appl. 15 pp 243– (1966) · Zbl 0139.10301 · doi:10.1016/0022-247X(66)90115-6 [2] Croft H. T., Unsolved problems in geometry (1991) · Zbl 0748.52001 · doi:10.1007/978-1-4612-0963-8 [3] Gay D. M., ACM Trans. Math. Software 9 (4) pp 503– (1983) · Zbl 0519.65039 · doi:10.1145/356056.356066 [4] Graham R. L., Discrete Math. 181 (1) pp 139– (1998) · Zbl 0901.52017 · doi:10.1016/S0012-365X(97)00050-2 [5] Hardin R. H., ”Spherical codes” · Zbl 0838.05027 [6] Heppes A., Period. Math. Hungar. 34 (1) pp 65– (1997) · Zbl 0880.52008 · doi:10.1023/A:1004224507766 [7] Lengyel A., ”Egységnégyzet lefedése egybevágó körökkel (Covering the unit square with congruent circles)” (1996) [8] Melissen H., Amer. Math. Monthly 100 (10) pp 916– (1993) · Zbl 0814.52006 · doi:10.2307/2324212 [9] Melissen H., Math. Mag. 70 pp 119– (1997) [10] Melissen H., Ph.D. thesis, in: Packing and covering with circles (1997) · Zbl 0880.52008 [11] Melissen J. B. M., Electron. J. Combin. 3 (1) pp R32– (1996) [12] Melissen J. B. M., Discrete Appl. Math. 99 (1) pp 149– (2000) · Zbl 0951.52017 · doi:10.1016/S0166-218X(99)00130-4 [13] Nurmela K. J., Discrete Comput. Geom. 18 (1) pp 111– (1997) · Zbl 0880.90116 · doi:10.1007/PL00009306 [14] Nurmela K. J., ”Covering a square with up to 30 equal circles” (2000) · Zbl 0986.52011 [15] Tarnai T., Elem. Math. 50 (4) pp 167– (1995) [16] Zahn C. T., J. Res. Nat. Bur. Standards Sect. B 66 pp 181– (1962) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.