-
1
-
-
84922470762
-
-
[arXiv]
-
[arXiv] http://xxx.lanl.gov.
-
-
-
-
2
-
-
33744745792
-
Bestimmung der grössten Anzahl gleich grosser Kugeln, welche sich auf eine Kugel von demselben Radius, wie die übrigen, auflegen lassen
-
[Ben]
-
[Ben] C. Bender, Bestimmung der grössten Anzahl gleich grosser Kugeln, welche sich auf eine Kugel von demselben Radius, wie die übrigen, auflegen lassen, Arch. Math. Phys. 56 (1874), 302-306.
-
(1874)
Arch. Math. Phys.
, vol.56
, pp. 302-306
-
-
Bender, C.1
-
3
-
-
33744770505
-
A remark on the packing density in the 3-space
-
[Bez1] eds. K. Böröczky and G. Fejes Tóth, Colloquia Mathematica Societati János Bolyai, North-Holland, Amsterdam
-
[Bez1] A. Bezdek, A remark on the packing density in the 3-space, in Intuitive Geometry, eds. K. Böröczky and G. Fejes Tóth, Colloquia Mathematica Societati János Bolyai, vol. 63, North-Holland, Amsterdam, 1994, pp. 17-22.
-
(1994)
Intuitive Geometry
, vol.63
, pp. 17-22
-
-
Bezdek, A.1
-
4
-
-
0031287909
-
Isoperimetric inequalities and the dodecahedral conjecture
-
[Bez2]
-
[Bez2] K. Bezdek, Isoperimetric inequalities and the dodecahedral conjecture, Internat. J.Math.8(6)(1997), 759-780.
-
(1997)
Internat. J.Math.
, vol.8
, Issue.6
, pp. 759-780
-
-
Bezdek, K.1
-
5
-
-
1842642893
-
Maximum density space packing with congruent circular cylinders of infinite length
-
[BK]
-
[BK] A. Bezdek and W. Kuperberg, Maximum density space packing with congruent circular cylinders of infinite length, Mathematica 37 (1990), 74-80.
-
(1990)
Mathematica
, vol.37
, pp. 74-80
-
-
Bezdek, A.1
Kuperberg, W.2
-
6
-
-
51649150531
-
Maximum density space packing with parallel strings of balls
-
[BKM]
-
[BKM] A. Bezdek, W. Kaperberg, and E. Makai Jr., Maximum density space packing with parallel strings of balls, Discrete Comput. Geom. 6 (1991), 227-283.
-
(1991)
Discrete Comput. Geom.
, vol.6
, pp. 227-283
-
-
Bezdek, A.1
Kaperberg, W.2
Makai Jr., E.3
-
7
-
-
33744777670
-
Report on the theory of the geometry of numbers
-
[Bl1]
-
[Bl1] H. F. Blichfeldt, Report on the theory of the geometry of numbers, Bull. Amer. Math. Soc. 25 (1919), 449-453.
-
(1919)
Bull. Amer. Math. Soc.
, vol.25
, pp. 449-453
-
-
Blichfeldt, H.F.1
-
8
-
-
0000386099
-
The minimum value of quadratic forms and the closest packing of spheres
-
[Bl2]
-
[Bl2] H. F. Blichfeldt, The minimum value of quadratic forms and the closest packing of spheres, Math. Ann. 101 (1929), 605-608.
-
(1929)
Math. Ann.
, vol.101
, pp. 605-608
-
-
Blichfeldt, H.F.1
-
9
-
-
0040933747
-
The minimum values of positive quadratic forms in six, seven and eight variables
-
[Bl3]
-
[Bl3] H. F. Blichfeldt, The minimum values of positive quadratic forms in six, seven and eight variables, Math. Z. 39 (1935), 1-15.
-
(1935)
Math. Z.
, vol.39
, pp. 1-15
-
-
Blichfeldt, H.F.1
-
10
-
-
0346564174
-
Some remarks concerning close-packing of equal spheres
-
[Bo]
-
[Bo] A. H. Boerdijk, Some remarks concerning close-packing of equal spheres, Philips Res. Rep. 7 (1952), 303-313.
-
(1952)
Philips Res. Rep.
, vol.7
, pp. 303-313
-
-
Boerdijk, A.H.1
-
11
-
-
33744762353
-
On the Kepler conjecture
-
[CHMS]
-
[CHMS] J. H. Conway, T. C. Hales, D. J. Muder, and N. J. A. Sloane, On the Kepler conjecture, Math. Intelligencer 16(2) (1994), 5.
-
(1994)
Math. Intelligencer
, vol.16
, Issue.2
, pp. 5
-
-
Conway, J.H.1
Hales, T.C.2
Muder, D.J.3
Sloane, N.J.A.4
-
13
-
-
51249169208
-
What are all the best sphere packings in low dimensions?
-
[CS1]
-
[CS1] J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions? Discrete Comput. Geom. 13 (1995), 383-403.
-
(1995)
Discrete Comput. Geom.
, vol.13
, pp. 383-403
-
-
Conway, J.H.1
Sloane, N.J.A.2
-
14
-
-
0003643241
-
-
[CS2] Springer-Verlag, New York
-
[CS2] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, third edition, Springer-Verlag, New York, 1998.
-
(1998)
Sphere Packings, Lattices and Groups, Third Edition
-
-
Conway, J.H.1
Sloane, N.J.A.2
-
16
-
-
0040355166
-
Recent progress on packing and covering
-
[Fej3] Contemporary Mathematics, AMS, Providence, RI, MR 99g:52036
-
[Fej3] G. Fejes Tóth, Recent progress on packing and covering, in Advances in Discrete and Computational Geometry (South Hadley, MA, 1996), Contemporary Mathematics, vol. 223, AMS, Providence, RI, 1999, pp. 145-162. MR 99g:52036.
-
(1999)
Advances in Discrete and Computational Geometry (South Hadley, MA, 1996)
, vol.223
, pp. 145-162
-
-
Tóth, G.F.1
-
17
-
-
0001214488
-
Über die dichteste Kugellagerung
-
[Fej4]
-
[Fej4] L. Fejes Tóth, Über die dichteste Kugellagerung, Math. Z. 48 (1942-1943), 676-684.
-
(1942)
Math. Z.
, vol.48
, pp. 676-684
-
-
Tóth, L.F.1
-
18
-
-
0013526298
-
Some packing and covering theorems
-
[Fej5]
-
[Fej5] L. Fejes Tóth, Some packing and covering theorems, Acta Sci. Math. (Szeded) 12/A (1950), 62-67.
-
(1950)
Acta Sci. Math. (Szeded)
, vol.12 A
, pp. 62-67
-
-
Tóth, L.F.1
-
20
-
-
0004230986
-
-
[Fej7] Pergamon Press, Oxford
-
[Fej7] L. Fejes Tóth, Regular Figures, Pergamon Press, Oxford, 1964.
-
(1964)
Regular Figures
-
-
Tóth, L.F.1
-
22
-
-
33646625348
-
-
[Fer] Thesis, University of Michigan
-
[Fer] S. P. Ferguson, Sphere Packings, V, Thesis, University of Michigan, 1997.
-
(1997)
Sphere Packings, V
-
-
Ferguson, S.P.1
-
24
-
-
2342607276
-
Untersuchungen über die Eigenscahften der positiven temären quadratischen Formen von Ludwig August Seher
-
[G] Juli 9
-
[G] C. F. Gauss, Untersuchungen über die Eigenscahften der positiven temären quadratischen Formen von Ludwig August Seher, Göttingische gelehrte Anzeigen, 1831 Juli 9,
-
(1831)
Göttingische Gelehrte Anzeigen
-
-
Gauss, C.F.1
-
25
-
-
0011008350
-
-
also published in J. Reine Angew. Math. 20 (1840), 312-320,
-
(1840)
J. Reine Angew. Math.
, vol.20
, pp. 312-320
-
-
-
26
-
-
2342607276
-
-
Königliche Gesellschaft der Wissenschaften, Göttingen
-
and Werke, vol. 2, Königliche Gesellschaft der Wissenschaften, Göttingen, 1876, pp. 188-196.
-
(1876)
Werke
, vol.2
, pp. 188-196
-
-
-
28
-
-
0013474954
-
Ein stereometrisches Problem
-
[Gu]
-
[Gu] S. Günther, Ein stereometrisches Problem, Arch. Math. Phys. 57 (1875), 209-215.
-
(1875)
Arch. Math. Phys.
, vol.57
, pp. 209-215
-
-
Günther, S.1
-
29
-
-
0002621472
-
The sphere packing problem
-
[Ha1]
-
[Ha1] T. C. Hales, The sphere packing problem, J. Comput. Appl. Math. 44 (1992), 41-76.
-
(1992)
J. Comput. Appl. Math.
, vol.44
, pp. 41-76
-
-
Hales, T.C.1
-
30
-
-
33745892705
-
Remarks on the density of sphere packings in three dimensions
-
[Ha2]
-
[Ha2] T. C. Hales, Remarks on the density of sphere packings in three dimensions, Combinatorica 13 (1993), 181-187.
-
(1993)
Combinatorica
, vol.13
, pp. 181-187
-
-
Hales, T.C.1
-
31
-
-
0002861691
-
The status of the Kepler conjecture
-
[Ha3]
-
[Ha3] T. C. Hales, The status of the Kepler conjecture, Math. Intelligencer 16(3) (1994), 47-58.
-
(1994)
Math. Intelligencer
, vol.16
, Issue.3
, pp. 47-58
-
-
Hales, T.C.1
-
32
-
-
84922439418
-
-
[Ha4]
-
[Ha4] T. C. Hales, http://www.pitt.edu/~thales/kepler98/holyoke.html.
-
-
-
Hales, T.C.1
-
33
-
-
0031538808
-
Sphere packings, I
-
[Ha6]
-
[Ha6] T. C. Hales, Sphere packings, I, Discrete Comput. Geom. 17 (1977), 1-51.
-
(1977)
Discrete Comput. Geom.
, vol.17
, pp. 1-51
-
-
Hales, T.C.1
-
34
-
-
0039918143
-
Sphere packings, II
-
[Ha7]
-
[Ha7] T. C. Hales, Sphere packings, II, Discrete Comput. Geom. 18 (1997), 135-149.
-
(1997)
Discrete Comput. Geom.
, vol.18
, pp. 135-149
-
-
Hales, T.C.1
-
38
-
-
0000491573
-
Cannonballs and honeycombs
-
[Ha12]
-
[Ha12] T. C. Hales, Cannonballs and honeycombs, Notices Amer. Math. Soc. 47(4), 440-449.
-
Notices Amer. Math. Soc.
, vol.47
, Issue.4
, pp. 440-449
-
-
Hales, T.C.1
-
40
-
-
33744768244
-
Some algorithms arising in the proof of the Kepler conjecture
-
[Ha14] Springer-Verlag, Berlin, July
-
[Ha14] T. C. Hales, Some algorithms arising in the proof of the Kepler conjecture, in Discrete and Computational Geometry, Algorithms and Combinatorics, vol. 25, Springer-Verlag, Berlin, July 2003, pp. 489-507.
-
(2003)
Discrete and Computational Geometry, Algorithms and Combinatorics
, vol.25
, pp. 489-507
-
-
Hales, T.C.1
-
41
-
-
0002849569
-
Mathematische Probleme
-
[Hi]
-
[Hi] D. Hilbert, Mathematische Probleme, Archiv Math. Phys. 1 (1901), 44-63,
-
(1901)
Archiv Math. Phys.
, vol.1
, pp. 44-63
-
-
Hilbert, D.1
-
42
-
-
0003356823
-
Mathematical Developments Arising from Hilbert Problems
-
AMS, Providence, RI
-
also in Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, vol. 28, AMS, Providence, RI, 1976, pp. 1-34.
-
(1976)
Proceedings of Symposia in Pure Mathematics
, vol.28
, pp. 1-34
-
-
-
43
-
-
0040773831
-
Bemerkung der Redaction
-
[Ho]
-
[Ho] R. Hoppe, Bemerkung der Redaction, Math. Phys. 56 (1874), 307-312.
-
(1874)
Math. Phys.
, vol.56
, pp. 307-312
-
-
Hoppe, R.1
-
44
-
-
0004216638
-
-
[HPT] Kluwer, Dordrecht
-
[HPT] R. Horst, P. M. Pardalos, and N. V. Thoai, Introduction to Global Optimization, Kluwer, Dordrecht, 1995.
-
(1995)
Introduction to Global Optimization
-
-
Horst, R.1
Pardalos, P.M.2
Thoai, N.V.3
-
45
-
-
0000120999
-
On the sphere packing problem and the proof of Kepler's conjecture
-
[Hs1]
-
[Hs1] W.-Y. Hsiang, On the sphere packing problem and the proof of Kepler's conjecture, Internat. J. Math. 93 (1993), 739-831.
-
(1993)
Internat. J. Math.
, vol.93
, pp. 739-831
-
-
Hsiang, W.-Y.1
-
46
-
-
33744730992
-
On the sphere packing problem and the proof of Kepler's conjecture
-
[Hs2] (Alghero, 1992), World Scientific, River Edge, NJ
-
[Hs2] W.-Y. Hsiang, On the sphere packing problem and the proof of Kepler's conjecture, in Differential Geometry and Topology (Alghero, 1992), World Scientific, River Edge, NJ, 1993, pp. 117-127.
-
(1993)
Differential Geometry and Topology
, pp. 117-127
-
-
Hsiang, W.-Y.1
-
47
-
-
33744735542
-
The geometry of spheres
-
[Hs3] (Shanghai, 1991), World Scientific, River Edge, NJ
-
[Hs3] W.-Y. Hsiang, The geometry of spheres, in Differential Geometry (Shanghai, 1991), World Scientific, River Edge, NJ, 1993, pp. 92-107.
-
(1993)
Differential Geometry
, pp. 92-107
-
-
Hsiang, W.-Y.1
-
48
-
-
0003150481
-
A rejoinder to T. C. Hales's article the status of the Kepler conjecture
-
[Hs4]
-
[Hs4] W.-Y. Hsiang, A rejoinder to T. C. Hales's article "The status of the Kepler conjecture," Math. Intelligencer 17(1) (1995), 35-42.
-
(1995)
Math. Intelligencer
, vol.17
, Issue.1
, pp. 35-42
-
-
Hsiang, W.-Y.1
-
51
-
-
0040198815
-
-
[Ke] Oxford University Press, Oxford, Foreword by L. L. Whyte
-
[Ke] J. Kepler, The Six-Cornered Snowflake, Oxford University Press, Oxford, 1966, Foreword by L. L. Whyte.
-
(1966)
The Six-cornered Snowflake
-
-
Kepler, J.1
-
52
-
-
0000836432
-
Sur les formes quadratiques
-
[KZ1]
-
[KZ1] A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366-389.
-
(1873)
Math. Ann.
, vol.6
, pp. 366-389
-
-
Korkine, A.1
Zolotareff, G.2
-
53
-
-
0040156836
-
Sur les formes quadratiques positives
-
[KZ2]
-
[KZ2] A. Korkine and G. Zolotareff, Sur les formes quadratiques positives, Math. Ann. 11 (1877), 242-292.
-
(1877)
Math. Ann.
, vol.11
, pp. 242-292
-
-
Korkine, A.1
Zolotareff, G.2
-
54
-
-
0345641591
-
Recherches d'arithmétique
-
[La] Gauthier-Villars, Paris
-
[La] J. L. Lagrange, Recherches d'arithmétique, Nov. Mem. Acad. Roy. Sc. Bell Lettres Berlin 1773, in Œuvres, vol. 3, Gauthier-Villars, Paris, 1867-1892, pp. 693-758.
-
(1867)
Nov. Mem. Acad. Roy. Sc. Bell Lettres Berlin 1773, in ŒUvres
, vol.3
, pp. 693-758
-
-
Lagrange, J.L.1
-
55
-
-
0001794073
-
The Problem of the thirteen spheres
-
[Le] Feb
-
[Le] J. Leech, The Problem of the thirteen spheres, Math. Gaz. 40 (Feb 1956), 22-23.
-
(1956)
Math. Gaz.
, vol.40
, pp. 22-23
-
-
Leech, J.1
-
60
-
-
0039747663
-
Hilbert's problem 18: On crystallographic groups, fundamental domains, and on sphere packings
-
[Mi] AMS, Providence, RI
-
[Mi] J. Milnor, Hilbert's problem 18: on crystallographic groups, fundamental domains, and on sphere packings, in Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pine Mathematics, vol. 28, AMS, Providence, RI, 1976, pp. 491-506.
-
(1976)
Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pine Mathematics
, vol.28
, pp. 491-506
-
-
Milnor, J.1
-
62
-
-
84963057017
-
Putting the best face on a Voronoi polyhedron
-
[Mu1]
-
[Mu1] D. J. Muder, Putting the best face on a Voronoi polyhedron, Proc. London Math. Soc. (3) 56 (1988), 329-348.
-
(1988)
Proc. London Math. Soc. (3)
, vol.56
, pp. 329-348
-
-
Muder, D.J.1
-
63
-
-
51249168300
-
A new bound on the local density of sphere packings
-
[Mu2]
-
[Mu2] D. J. Muder A new bound on the local density of sphere packings, Discrete Comput. Geom. 10 (1993), 351-375.
-
(1993)
Discrete Comput. Geom.
, vol.10
, pp. 351-375
-
-
Muder, D.J.1
-
64
-
-
33744740030
-
Letter
-
[Mu3] by S. Singh, Walker, New York
-
[Mu3] D. J. Muder, Letter, in Fermat's Enigma, by S. Singh, Walker, New York, 1997.
-
(1997)
Fermat's Enigma
-
-
Muder, D.J.1
-
65
-
-
4244118487
-
Empilements de sphères, Séminaire Bourbaki
-
[O] No. 189-190 exp. no. 727
-
[O] J. Oesterlé, Empilements de sphères, Séminaire Bourbaki, vol. 1989/90, Astérisque, No. 189-190 exp. no. 727, (1990), 375-397.
-
(1990)
Astérisque
, vol.1989
, Issue.90
, pp. 375-397
-
-
Oesterlé, J.1
-
66
-
-
84922439417
-
-
[P] K. Plofker, Private communication, January 2000
-
[P] K. Plofker, Private communication, January 2000.
-
-
-
-
69
-
-
0000665771
-
The packing of equal spheres
-
[Ro1]
-
[Ro1] C. A. Rogers, The packing of equal spheres, Proc. London Math. Soc. (3) 8 (1958), 609-620.
-
(1958)
Proc. London Math. Soc. (3)
, vol.8
, pp. 609-620
-
-
Rogers, C.A.1
-
70
-
-
0004279601
-
-
[Ro2] Cambridge University Press, Cambridge
-
[Ro2] C. A. Rogers, Packing and Covering, Cambridge University Press, Cambridge, 1964.
-
(1964)
Packing and Covering
-
-
Rogers, C.A.1
-
72
-
-
21844495969
-
Minimal-energy clusters of hard spheres
-
[SHDC]
-
[SHDC] N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, Minimal-energy clusters of hard spheres, Discrete Comput. Geom. 14(3) (1995), 237-259.
-
(1995)
Discrete Comput. Geom.
, vol.14
, Issue.3
, pp. 237-259
-
-
Sloane, N.J.A.1
Hardin, R.H.2
Duff, T.D.S.3
Conway, J.H.4
-
73
-
-
33744731322
-
On the densest packing of circles
-
[SM]
-
[SM] B. Segre and K. Mahler, On the densest packing of circles, Amer. Math Monthly (1944), 261-270.
-
(1944)
Amer. Math Monthly
, pp. 261-270
-
-
Segre, B.1
Mahler, K.2
-
74
-
-
34250943898
-
Das Problem der dreizehn Kugeln
-
[SW]
-
[SW] K. Schütte and B.L. van der Waerden, Das Problem der dreizehn Kugeln, Math. Ann. 125 (1953), 325-334.
-
(1953)
Math. Ann.
, vol.125
, pp. 325-334
-
-
Schütte, K.1
Van Der Waerden, B.L.2
-
76
-
-
0038972605
-
Om nogle geometrisk taltheoretiske Theoremer
-
[T1]
-
[T1] A. Thue, Om nogle geometrisk taltheoretiske Theoremer, Forand. Skand. Natur. 14 (1892), 352-353.
-
(1892)
Forand. Skand. Natur.
, vol.14
, pp. 352-353
-
-
Thue, A.1
-
77
-
-
0006569732
-
Über die dichteste Zusammenstellung von kongruenten Kreisen in der Ebene
-
[T2]
-
[T2] A. Thue, Über die dichteste Zusammenstellung von kongruenten Kreisen in der Ebene, Christinia Vid. Seist. Skr. 1 (1910), 1-9.
-
(1910)
Christinia Vid. Seist. Skr.
, vol.1
, pp. 1-9
-
-
Thue, A.1
-
78
-
-
84922439416
-
-
[W] L. L. Whyte, Foreword to [Ke]
-
[W] L. L. Whyte, Foreword to [Ke].
-
-
-
|