Sphere packing (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Sphere packing" in English language version.

refsWebsite

Global rank English rank

22doi.org

2^nd place

16arxiv.org

69^th place

59^th place

6harvard.edu

18^th place

17^th place

4ams.org

451^st place

277^th place

3quantamagazine.org

6,413^th place

4,268^th place

2handle.net

102^nd place

76^th place

2wolfram.com

513^th place

537^th place

2nih.gov

4^th place

2princeton.edu

741^st place

577^th place

1hal.science

low place

1code.google.com

4,942^nd place

4,061^st place

1zbmath.org

1,923^rd place

1,068^th place

1youtube.com

9^th place

13^th place

1ghostarchive.org

32^nd place

21^st place

1tandfonline.com

507^th place

429^th place

1emis.de

low place

1americanscientist.org

7,231^st place

5,635^th place

1books.google.com

3^rd place

americanscientist.org (Global: 7,231^st place; English: 5,635^th place)

Hayes, Brian (6 February 2017). "The Science of Sticky Spheres". American Scientist. Retrieved 14 July 2020.

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Cohn, Henry; Kumar, Abhinav (2009). "Optimality and uniqueness of the Leech lattice among lattices". Annals of Mathematics. 170 (3): 1003–1050. arXiv:math.MG/0403263. doi:10.4007/annals.2009.170.1003. MR 2600869. Zbl 1213.11144. Cohn, Henry; Kumar, Abhinav (2004). "The densest lattice in twenty-four dimensions". Electronic Research Announcements of the American Mathematical Society. 10 (7): 58–67. arXiv:math.MG/0408174. doi:10.1090/S1079-6762-04-00130-1. MR 2075897.
Cohn, Henry (2017). "A conceptual breakthrough in sphere packing" (PDF). Notices of the American Mathematical Society. 64 (2): 102–115. arXiv:1611.01685. doi:10.1090/noti1474. MR 3587715.
Torquato, S.; Stillinger, F. H. (2006). "New conjectural lower bounds on the optimal density of sphere packings". Experimental Mathematics. 15 (3): 307–331. arXiv:math/0508381. doi:10.1080/10586458.2006.10128964. MR 2264469.

ams.org

Cohn, Henry (2017). "A conceptual breakthrough in sphere packing" (PDF). Notices of the American Mathematical Society. 64 (2): 102–115. arXiv:1611.01685. doi:10.1090/noti1474. MR 3587715.

arxiv.org (Global: 69^th place; English: 59^th place)

Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. hdl:1959.4/unsworks_66615.
Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184.
Farrell, Greg R.; Martini, K. Michael; Menon, Narayanan (2010). "Loose packings of frictional spheres". Soft Matter. 6 (13): 2925. arXiv:1005.0804. Bibcode:2010SMat....6.2925F. doi:10.1039/C0SM00038H.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438.
Sloane, N. J. A. (1998). "The Sphere-Packing Problem". Documenta Mathematica. 3: 387–396. arXiv:math/0207256.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. hdl:21.11116/0000-0004-08A3-B.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8.
Cohn, Henry; Kumar, Abhinav (2009). "Optimality and uniqueness of the Leech lattice among lattices". Annals of Mathematics. 170 (3): 1003–1050. arXiv:math.MG/0403263. doi:10.4007/annals.2009.170.1003. MR 2600869. Zbl 1213.11144. Cohn, Henry; Kumar, Abhinav (2004). "The densest lattice in twenty-four dimensions". Electronic Research Announcements of the American Mathematical Society. 10 (7): 58–67. arXiv:math.MG/0408174. doi:10.1090/S1079-6762-04-00130-1. MR 2075897.
Cohn, Henry (2017). "A conceptual breakthrough in sphere packing" (PDF). Notices of the American Mathematical Society. 64 (2): 102–115. arXiv:1611.01685. doi:10.1090/noti1474. MR 3587715.
Torquato, S.; Stillinger, F. H. (2006). "New conjectural lower bounds on the optimal density of sphere packings". Experimental Mathematics. 15 (3): 307–331. arXiv:math/0508381. doi:10.1080/10586458.2006.10128964. MR 2264469.
Campos, Marcelo; Jenssen, Matthew; Michelen, Marcus; Sahasrabudhe, Julian (2023). "A new lower bound for sphere packing". arXiv:2312.10026 [math.MG].
Klartag, Boaz (2025). "Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid". arXiv:2504.05042 [math.MG].
de Laat, David; de Oliveira Filho, Fernando Mário; Vallentin, Frank (12 June 2012). "Upper bounds for packings of spheres of several radii". Forum of Mathematics, Sigma. 2 e23. arXiv:1206.2608. doi:10.1017/fms.2014.24.
Dennis, Robert; Corwin, Eric (2 September 2021). "Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities". Physical Review. 128 (1) 018002. arXiv:2006.11415. doi:10.1103/PhysRevLett.128.018002. PMID 35061468.
Kozma, R. T.; Szirmai, J. (2012). "Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types". Monatshefte für Mathematik. 168: 27–47. arXiv:1007.0722. doi:10.1007/s00605-012-0393-x.
Bezdek, Karoly; Reid, Samuel (2013). "Contact Graphs of Sphere Packings Revisited". Journal of Geometry. 104 (1): 57–83. arXiv:1210.5756. doi:10.1007/s00022-013-0156-4.

books.google.com (Global: 3^rd place; English: 3^rd place)

Conway, John H.; Sloane, Neil J. A. (1998). Sphere Packings, Lattices and Groups (3rd ed.). Springer Science & Business Media. ISBN 0-387-98585-9.

code.google.com (Global: 4,942^nd place; English: 4,061^st place)

"Long-term storage for Google Code Project Hosting". Google Code Archive.

doi.org (Global: 2^nd place; English: 2^nd place)

Wu, Yugong; Fan, Zhigang; Lu, Yuzhu (1 May 2003). "Bulk and interior packing densities of random close packing of hard spheres". Journal of Materials Science. 38 (9): 2019–2025. doi:10.1023/A:1023597707363.
Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. hdl:1959.4/unsworks_66615.
Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184.
Farrell, Greg R.; Martini, K. Michael; Menon, Narayanan (2010). "Loose packings of frictional spheres". Soft Matter. 6 (13): 2925. arXiv:1005.0804. Bibcode:2010SMat....6.2925F. doi:10.1039/C0SM00038H.
Chaikin, Paul (June 2007). "Random thoughts". Physics Today. 60 (6). American Institute of Physics: 8. Bibcode:2007PhT....60f...8C. doi:10.1063/1.2754580.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438.
Griffith, J.S. (1962). "Packing of equal 0-spheres". Nature. 196 (4856): 764–765. Bibcode:1962Natur.196..764G. doi:10.1038/196764a0.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. hdl:21.11116/0000-0004-08A3-B.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8.
Cohn, Henry; Kumar, Abhinav (2009). "Optimality and uniqueness of the Leech lattice among lattices". Annals of Mathematics. 170 (3): 1003–1050. arXiv:math.MG/0403263. doi:10.4007/annals.2009.170.1003. MR 2600869. Zbl 1213.11144. Cohn, Henry; Kumar, Abhinav (2004). "The densest lattice in twenty-four dimensions". Electronic Research Announcements of the American Mathematical Society. 10 (7): 58–67. arXiv:math.MG/0408174. doi:10.1090/S1079-6762-04-00130-1. MR 2075897.
Cohn, Henry (2017). "A conceptual breakthrough in sphere packing" (PDF). Notices of the American Mathematical Society. 64 (2): 102–115. arXiv:1611.01685. doi:10.1090/noti1474. MR 3587715.
Torquato, S.; Stillinger, F. H. (2006). "New conjectural lower bounds on the optimal density of sphere packings". Experimental Mathematics. 15 (3): 307–331. arXiv:math/0508381. doi:10.1080/10586458.2006.10128964. MR 2264469.
O'Toole, P. I.; Hudson, T. S. (2011). "New High-Density Packings of Similarly Sized Binary Spheres". The Journal of Physical Chemistry C. 115 (39): 19037. doi:10.1021/jp206115p.
Hudson, D. R. (1949). "Density and Packing in an Aggregate of Mixed Spheres". Journal of Applied Physics. 20 (2): 154–162. Bibcode:1949JAP....20..154H. doi:10.1063/1.1698327.
Zong, C. (2002). "From deep holes to free planes". Bulletin of the American Mathematical Society. 39 (4): 533–555. doi:10.1090/S0273-0979-02-00950-3.
de Laat, David; de Oliveira Filho, Fernando Mário; Vallentin, Frank (12 June 2012). "Upper bounds for packings of spheres of several radii". Forum of Mathematics, Sigma. 2 e23. arXiv:1206.2608. doi:10.1017/fms.2014.24.
Dennis, Robert; Corwin, Eric (2 September 2021). "Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities". Physical Review. 128 (1) 018002. arXiv:2006.11415. doi:10.1103/PhysRevLett.128.018002. PMID 35061468.
Bowen, L.; Radin, C. (2002). "Densest Packing of Equal Spheres in Hyperbolic Space". Discrete and Computational Geometry. 29: 23–39. doi:10.1007/s00454-002-2791-7.
Böröczky, K. (1978). "Packing of spheres in spaces of constant curvature". Acta Mathematica Academiae Scientiarum Hungaricae. 32 (3–4): 243–261. doi:10.1007/BF01902361.
Böröczky, K.; Florian, A. (1964). "Über die dichteste Kugelpackung im hyperbolischen Raum". Acta Mathematica Academiae Scientiarum Hungaricae. 15 (1–2): 237–245. doi:10.1007/BF01897041.
Kozma, R. T.; Szirmai, J. (2012). "Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types". Monatshefte für Mathematik. 168: 27–47. arXiv:1007.0722. doi:10.1007/s00605-012-0393-x.
Bezdek, Karoly; Reid, Samuel (2013). "Contact Graphs of Sphere Packings Revisited". Journal of Geometry. 104 (1): 57–83. arXiv:1210.5756. doi:10.1007/s00022-013-0156-4.

emis.de (Global: low place; English: low place)

Marshall, G. W.; Hudson, T. S. (2010). "Dense binary sphere packings". Contributions to Algebra and Geometry. 51 (2): 337–344.

ghostarchive.org (Global: 32^nd place; English: 21^st place)

Miller, Stephen D. (4 April 2016). "The solution to the sphere packing problem in 24 dimensions via modular forms". Institute for Advanced Study. Archived from the original on 21 December 2021.. Video of an hour-long talk by one of Viazovska's co-authors explaining the new proofs.

hal.science (Global: low place; English: low place)

Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. hdl:1959.4/unsworks_66615.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. hdl:1959.4/unsworks_66615.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. hdl:21.11116/0000-0004-08A3-B.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184.
Farrell, Greg R.; Martini, K. Michael; Menon, Narayanan (2010). "Loose packings of frictional spheres". Soft Matter. 6 (13): 2925. arXiv:1005.0804. Bibcode:2010SMat....6.2925F. doi:10.1039/C0SM00038H.
Chaikin, Paul (June 2007). "Random thoughts". Physics Today. 60 (6). American Institute of Physics: 8. Bibcode:2007PhT....60f...8C. doi:10.1063/1.2754580.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438.
Griffith, J.S. (1962). "Packing of equal 0-spheres". Nature. 196 (4856): 764–765. Bibcode:1962Natur.196..764G. doi:10.1038/196764a0.
Hudson, D. R. (1949). "Density and Packing in an Aggregate of Mixed Spheres". Journal of Applied Physics. 20 (2): 154–162. Bibcode:1949JAP....20..154H. doi:10.1063/1.1698327.

nih.gov (Global: 4^th place; English: 4^th place)

pubmed.ncbi.nlm.nih.gov

Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438.
Dennis, Robert; Corwin, Eric (2 September 2021). "Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities". Physical Review. 128 (1) 018002. arXiv:2006.11415. doi:10.1103/PhysRevLett.128.018002. PMID 35061468.

princeton.edu (Global: 741^st place; English: 577^th place)

annals.math.princeton.edu

Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. hdl:21.11116/0000-0004-08A3-B.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8.

quantamagazine.org (Global: 6,413^th place; English: 4,268^th place)

Klarreich, Erica (30 March 2016). "Sphere Packing Solved in Higher Dimensions". Quanta Magazine.
Houston-Edwards, Kelsey (30 April 2024). "To Pack Spheres Tightly, Mathematicians Throw Them at Random". Quanta Magazine. Retrieved 30 April 2024.
Howlett, Joseph (7 July 2025). "New Sphere-Packing Record Stems From an Unexpected Source". Quanta Magazine. Retrieved 7 July 2025.

tandfonline.com (Global: 507^th place; English: 429^th place)

Torquato, S.; Stillinger, F. H. (2006). "New conjectural lower bounds on the optimal density of sphere packings". Experimental Mathematics. 15 (3): 307–331. arXiv:math/0508381. doi:10.1080/10586458.2006.10128964. MR 2264469.

wolfram.com (Global: 513^th place; English: 537^th place)

mathworld.wolfram.com

youtube.com (Global: 9^th place; English: 13^th place)

Miller, Stephen D. (4 April 2016). "The solution to the sphere packing problem in 24 dimensions via modular forms". Institute for Advanced Study. Archived from the original on 21 December 2021.. Video of an hour-long talk by one of Viazovska's co-authors explaining the new proofs.

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Cohn, Henry; Kumar, Abhinav (2009). "Optimality and uniqueness of the Leech lattice among lattices". Annals of Mathematics. 170 (3): 1003–1050. arXiv:math.MG/0403263. doi:10.4007/annals.2009.170.1003. MR 2600869. Zbl 1213.11144. Cohn, Henry; Kumar, Abhinav (2004). "The densest lattice in twenty-four dimensions". Electronic Research Announcements of the American Mathematical Society. 10 (7): 58–67. arXiv:math.MG/0408174. doi:10.1090/S1079-6762-04-00130-1. MR 2075897.

Sphere packing (English Wikipedia)

americanscientist.org (Global: 7,231st place; English: 5,635th place)

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

ams.org

arxiv.org (Global: 69th place; English: 59th place)

books.google.com (Global: 3rd place; English: 3rd place)

code.google.com (Global: 4,942nd place; English: 4,061st place)

doi.org (Global: 2nd place; English: 2nd place)

emis.de (Global: low place; English: low place)

ghostarchive.org (Global: 32nd place; English: 21st place)