Borromean rings (English Wikipedia)

Chamberland, Marc; Herman, Eugene A. (2015), "Rock-paper-scissors meets Borromean rings", The Mathematical Intelligencer, 37 (2): 20–25, doi:10.1007/s00283-014-9499-4, MR 3356112, S2CID 558993
Rolfsen, Dale (1990), Knots and Links, Mathematics Lecture Series, vol. 7 (2nd ed.), Publish or Perish, Inc., Houston, TX, p. 425, ISBN 0-914098-16-0, MR 1277811
Conway, J. H. (1970), "An enumeration of knots and links, and some of their algebraic properties", Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967), Oxford: Pergamon, pp. 329–358, MR 0258014; see description of notation, pp. 332–333, and second line of table, p. 348.
Jablan, Slavik V. (1999), "Are Borromean links so rare?", Proceedings of the 2nd International Katachi U Symmetry Symposium, Part 1 (Tsukuba, 1999), Forma, 14 (4): 269–277, MR 1770213
Aravind, P. K. (1997), "Borromean entanglement of the GHZ state" (PDF), in Cohen, R. S.; Horne, M.; Stachel, J. (eds.), Potentiality, Entanglement and Passion-at-a-Distance, Boston Studies in the Philosophy of Science, Springer, pp. 53–59, doi:10.1007/978-94-017-2732-7_4, MR 1739812
Bai, Sheng; Wang, Weibiao (2020), "New criteria and constructions of Brunnian links", Journal of Knot Theory and Its Ramifications, 29 (13): 2043008, 27, arXiv:2006.10290, doi:10.1142/S0218216520430087, MR 4213076, S2CID 219792382
Thistlethwaite, Morwen B. (1991), "On the algebraic part of an alternating link", Pacific Journal of Mathematics, 151 (2): 317–333, doi:10.2140/pjm.1991.151.317, MR 1132393
Tverberg, Helge (2010), "On Borromean rings" (PDF), The Mathematical Scientist, 35 (1): 57–60, MR 2668444, archived from the original (PDF) on 2021-03-16, retrieved 2021-03-16
Howards, Hugh Nelson (2013), "Forming the Borromean rings out of arbitrary polygonal unknots", Journal of Knot Theory and Its Ramifications, 22 (14): 1350083, 15, arXiv:1406.3370, doi:10.1142/S0218216513500831, MR 3190121, S2CID 119674622
Burgiel, H.; Franzblau, D. S.; Gutschera, K. R. (1996), "The mystery of the linked triangles", Mathematics Magazine, 69 (2): 94–102, doi:10.1080/0025570x.1996.11996399, JSTOR 2690662, MR 1394792
Cantarella, Jason; Fu, Joseph H. G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C. (2006), "Criticality for the Gehring link problem" (PDF), Geometry & Topology, 10 (4): 2055–2116, arXiv:math/0402212, doi:10.2140/gt.2006.10.2055, MR 2284052
Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891
Uberti, R.; Janse van Rensburg, E. J.; Orlandini, E.; Tesi, M. C.; Whittington, S. G. (1998), "Minimal links in the cubic lattice", in Whittington, Stuart G.; Sumners, Witt De; Lodge, Timothy (eds.), Topology and Geometry in Polymer Science, IMA Volumes in Mathematics and its Applications, vol. 103, New York: Springer, pp. 89–100, doi:10.1007/978-1-4612-1712-1_9, MR 1655039; see Table 2, p. 97
Riley, Robert (1979), "An elliptical path from parabolic representations to hyperbolic structures", in Fenn, Roger (ed.), Topology of Low-Dimensional Manifolds: Proceedings of the Second Sussex Conference, 1977, Lecture Notes in Mathematics, vol. 722, Springer, pp. 99–133, doi:10.1007/BFb0063194, ISBN 978-3-540-09506-4, MR 0547459
Ratcliffe, John G. (2006), "The Borromean rings complement", Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics, vol. 149 (2nd ed.), Springer, pp. 459–461, ISBN 978-0-387-33197-3, MR 2249478
Hilden, Hugh M.; Lozano, María Teresa; Montesinos, José María (1983), "The Whitehead link, the Borromean rings and the knot 9₄₆ are universal", Seminario Matemático de Barcelona, 34 (1): 19–28, MR 0747855
Vogel, Denis (2005), Masseyprodukte in der Galoiskohomologie von Zahlkörpern [Massey products in the Galois cohomology of number fields], Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005, Göttingen: Universitätsdrucke Göttingen, pp. 93–98, doi:10.11588/heidok.00004418, MR 2206880
Morishita, Masanori (2010), "Analogies between knots and primes, 3-manifolds and number rings", Sugaku Expositions, 23 (1): 1–30, arXiv:0904.3399, MR 2605747

appliedprobability.org

Tverberg, Helge (2010), "On Borromean rings" (PDF), The Mathematical Scientist, 35 (1): 57–60, MR 2668444, archived from the original (PDF) on 2021-03-16, retrieved 2021-03-16

archive.org

Crum Brown, Alexander (December 1885), "On a case of interlacing surfaces", Proceedings of the Royal Society of Edinburgh, 13: 382–386
Didron, Adolphe Napoléon (1843), Iconographie Chrétienne (in French), Paris: Imprimerie Royale, pp. 568–569
"Mandala", Principia Discordia (4th ed.), March 1970, p. 43

arxiv.org

Bai, Sheng; Wang, Weibiao (2020), "New criteria and constructions of Brunnian links", Journal of Knot Theory and Its Ramifications, 29 (13): 2043008, 27, arXiv:2006.10290, doi:10.1142/S0218216520430087, MR 4213076, S2CID 219792382
Howards, Hugh Nelson (2013), "Forming the Borromean rings out of arbitrary polygonal unknots", Journal of Knot Theory and Its Ramifications, 22 (14): 1350083, 15, arXiv:1406.3370, doi:10.1142/S0218216513500831, MR 3190121, S2CID 119674622
Cantarella, Jason; Fu, Joseph H. G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C. (2006), "Criticality for the Gehring link problem" (PDF), Geometry & Topology, 10 (4): 2055–2116, arXiv:math/0402212, doi:10.2140/gt.2006.10.2055, MR 2284052
Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891
Morishita, Masanori (2010), "Analogies between knots and primes, 3-manifolds and number rings", Sugaku Expositions, 23 (1): 1–30, arXiv:0904.3399, MR 2605747
Kraemer, T.; Mark, M.; Waldburger, P.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Nägerl, H.-C.; Grimm, R. (2006), "Evidence for Efimov quantum states in an ultracold gas of caesium atoms", Nature, 440 (7082): 315–318, arXiv:cond-mat/0512394, Bibcode:2006Natur.440..315K, doi:10.1038/nature04626, PMID 16541068, S2CID 4379828

books.google.com

Rolfsen, Dale (1990), Knots and Links, Mathematics Lecture Series, vol. 7 (2nd ed.), Publish or Perish, Inc., Houston, TX, p. 425, ISBN 0-914098-16-0, MR 1277811
Ragland-Sullivan, Ellie; Milovanovic, Dragan (2004), "Introduction: Topologically Speaking", Lacan: Topologically Speaking, Other Press, ISBN 978-1-892746-76-4
Ratcliffe, John G. (2006), "The Borromean rings complement", Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics, vol. 149 (2nd ed.), Springer, pp. 459–461, ISBN 978-0-387-33197-3, MR 2249478
Ashley, Clifford Warren (1993) [1944], The Ashley Book of Knots, Doubleday, p. 354, ISBN 978-0-385-04025-9

bridgesmathart.org

archive.bridgesmathart.org

Gunn, Charles; Sullivan, John M. (2008), "The Borromean Rings: A video about the New IMU logo", in Sarhangi, Reza; Séquin, Carlo H. (eds.), Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, London: Tarquin Publications, pp. 63–70, ISBN 978-0-9665201-9-4; see the video itself at "The Borromean Rings: A new logo for the IMU Archived 2021-03-08 at the Wayback Machine" [w/video], International Mathematical Union

doi.org

Cromwell, Peter; Beltrami, Elisabetta; Rampichini, Marta (March 1998), "The Borromean rings", The mathematical tourist, The Mathematical Intelligencer, 20 (1): 53–62, doi:10.1007/bf03024401, S2CID 189888135
Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 15: The Borromean Rings Don't Exist", Proofs from THE BOOK (6th ed.), Springer, pp. 99–106, doi:10.1007/978-3-662-57265-8_15, ISBN 978-3-662-57265-8
Chamberland, Marc; Herman, Eugene A. (2015), "Rock-paper-scissors meets Borromean rings", The Mathematical Intelligencer, 37 (2): 20–25, doi:10.1007/s00283-014-9499-4, MR 3356112, S2CID 558993
Schoeck, Richard J. (Spring 1968), "Mathematics and the languages of literary criticism", The Journal of Aesthetics and Art Criticism, 26 (3): 367–376, doi:10.2307/429121, JSTOR 429121
Bruns, Carson J.; Stoddart, J. Fraser (2011), "The mechanical bond: A work of art", in Fabbrizzi, L. (ed.), Beauty in Chemistry, Topics in Current Chemistry, vol. 323, Springer, pp. 19–72, doi:10.1007/128_2011_296, PMID 22183145
Lakshminarayan, Arul (May 2007), "Borromean triangles and prime knots in an ancient temple", Resonance, 12 (5): 41–47, doi:10.1007/s12045-007-0049-7, S2CID 120259064
Aravind, P. K. (1997), "Borromean entanglement of the GHZ state" (PDF), in Cohen, R. S.; Horne, M.; Stachel, J. (eds.), Potentiality, Entanglement and Passion-at-a-Distance, Boston Studies in the Philosophy of Science, Springer, pp. 53–59, doi:10.1007/978-94-017-2732-7_4, MR 1739812
Glick, Ned (September 1999), "The 3-ring symbol of Ballantine Beer", The mathematical tourist, The Mathematical Intelligencer, 21 (4): 15–16, doi:10.1007/bf03025332, S2CID 123311380
Baird, Joseph L. (1970), "Unferth the þyle", Medium Ævum, 39 (1): 1–12, doi:10.2307/43631234, JSTOR 43631234, the stone bears also representations of three horns interlaced
Bai, Sheng; Wang, Weibiao (2020), "New criteria and constructions of Brunnian links", Journal of Knot Theory and Its Ramifications, 29 (13): 2043008, 27, arXiv:2006.10290, doi:10.1142/S0218216520430087, MR 4213076, S2CID 219792382
Nanyes, Ollie (October 1993), "An elementary proof that the Borromean rings are non-splittable", American Mathematical Monthly, 100 (8): 786–789, doi:10.2307/2324788, JSTOR 2324788
Thistlethwaite, Morwen B. (1991), "On the algebraic part of an alternating link", Pacific Journal of Mathematics, 151 (2): 317–333, doi:10.2140/pjm.1991.151.317, MR 1132393
Freedman, Michael H.; Skora, Richard (1987), "Strange actions of groups on spheres", Journal of Differential Geometry, 25: 75–98, doi:10.4310/jdg/1214440725; see in particular Lemma 3.2, p. 89
Lindström, Bernt; Zetterström, Hans-Olov (1991), "Borromean circles are impossible", American Mathematical Monthly, 98 (4): 340–341, doi:10.2307/2323803, JSTOR 2323803. Note however that Gunn & Sullivan (2008) write that this reference "seems to incorrectly deal only with the case that the three-dimensional configuration has a projection homeomorphic to" the conventional three-circle drawing of the link.
Howards, Hugh Nelson (2013), "Forming the Borromean rings out of arbitrary polygonal unknots", Journal of Knot Theory and Its Ramifications, 22 (14): 1350083, 15, arXiv:1406.3370, doi:10.1142/S0218216513500831, MR 3190121, S2CID 119674622
Burgiel, H.; Franzblau, D. S.; Gutschera, K. R. (1996), "The mystery of the linked triangles", Mathematics Magazine, 69 (2): 94–102, doi:10.1080/0025570x.1996.11996399, JSTOR 2690662, MR 1394792
Cantarella, Jason; Fu, Joseph H. G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C. (2006), "Criticality for the Gehring link problem" (PDF), Geometry & Topology, 10 (4): 2055–2116, arXiv:math/0402212, doi:10.2140/gt.2006.10.2055, MR 2284052
Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891
Uberti, R.; Janse van Rensburg, E. J.; Orlandini, E.; Tesi, M. C.; Whittington, S. G. (1998), "Minimal links in the cubic lattice", in Whittington, Stuart G.; Sumners, Witt De; Lodge, Timothy (eds.), Topology and Geometry in Polymer Science, IMA Volumes in Mathematics and its Applications, vol. 103, New York: Springer, pp. 89–100, doi:10.1007/978-1-4612-1712-1_9, MR 1655039; see Table 2, p. 97
Riley, Robert (1979), "An elliptical path from parabolic representations to hyperbolic structures", in Fenn, Roger (ed.), Topology of Low-Dimensional Manifolds: Proceedings of the Second Sussex Conference, 1977, Lecture Notes in Mathematics, vol. 722, Springer, pp. 99–133, doi:10.1007/BFb0063194, ISBN 978-3-540-09506-4, MR 0547459
Abbott, Steve (July 1997), "Review of Not Knot and Supplement to Not Knot", The Mathematical Gazette, 81 (491): 340–342, doi:10.2307/3619248, JSTOR 3619248, S2CID 64589738
Vogel, Denis (2005), Masseyprodukte in der Galoiskohomologie von Zahlkörpern [Massey products in the Galois cohomology of number fields], Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005, Göttingen: Universitätsdrucke Göttingen, pp. 93–98, doi:10.11588/heidok.00004418, MR 2206880
Chichak, Kelly S.; Cantrill, Stuart J.; Pease, Anthony R.; Chiu, Sheng-Hsien; Cave, Gareth W. V.; Atwood, Jerry L.; Stoddart, J. Fraser (May 28, 2004), "Molecular Borromean rings" (PDF), Science, 304 (5675): 1308–1312, Bibcode:2004Sci...304.1308C, doi:10.1126/science.1096914, PMID 15166376, S2CID 45191675
Mao, C.; Sun, W.; Seeman, N. C. (1997), "Assembly of Borromean rings from DNA", Nature, 386 (6621): 137–138, Bibcode:1997Natur.386..137M, doi:10.1038/386137b0, PMID 9062186, S2CID 4321733
Natarajan, Ganapati; Mathew, Ammu; Negishi, Yuichi; Whetten, Robert L.; Pradeep, Thalappil (2015-12-02), "A unified framework for understanding the structure and modifications of atomically precise monolayer protected gold clusters", The Journal of Physical Chemistry C, 119 (49): 27768–27785, doi:10.1021/acs.jpcc.5b08193, ISSN 1932-7447
Kumar, Vijith; Pilati, Tullio; Terraneo, Giancarlo; Meyer, Franck; Metrangolo, Pierangelo; Resnati, Giuseppe (2017), "Halogen bonded Borromean networks by design: topology invariance and metric tuning in a library of multi-component systems", Chemical Science, 8 (3): 1801–1810, doi:10.1039/C6SC04478F, PMC 5477818, PMID 28694953
Veliks, Janis; Seifert, Helen M.; Frantz, Derik K.; Klosterman, Jeremy K.; Tseng, Jui-Chang; Linden, Anthony; Siegel, Jay S. (2016), "Towards the molecular Borromean link with three unequal rings: double-threaded ruthenium(ii) ring-in-ring complexes", Organic Chemistry Frontiers, 3 (6): 667–672, doi:10.1039/c6qo00025h
Kraemer, T.; Mark, M.; Waldburger, P.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Nägerl, H.-C.; Grimm, R. (2006), "Evidence for Efimov quantum states in an ultracold gas of caesium atoms", Nature, 440 (7082): 315–318, arXiv:cond-mat/0512394, Bibcode:2006Natur.440..315K, doi:10.1038/nature04626, PMID 16541068, S2CID 4379828
Tanaka, K. (2010), "Observation of a Large Reaction Cross Section in the Drip-Line Nucleus ²²C", Physical Review Letters, 104 (6): 062701, Bibcode:2010PhRvL.104f2701T, doi:10.1103/PhysRevLett.104.062701, PMID 20366816, S2CID 7951719

harvard.edu

ui.adsabs.harvard.edu

Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891
Chichak, Kelly S.; Cantrill, Stuart J.; Pease, Anthony R.; Chiu, Sheng-Hsien; Cave, Gareth W. V.; Atwood, Jerry L.; Stoddart, J. Fraser (May 28, 2004), "Molecular Borromean rings" (PDF), Science, 304 (5675): 1308–1312, Bibcode:2004Sci...304.1308C, doi:10.1126/science.1096914, PMID 15166376, S2CID 45191675
Mao, C.; Sun, W.; Seeman, N. C. (1997), "Assembly of Borromean rings from DNA", Nature, 386 (6621): 137–138, Bibcode:1997Natur.386..137M, doi:10.1038/386137b0, PMID 9062186, S2CID 4321733
Kraemer, T.; Mark, M.; Waldburger, P.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Nägerl, H.-C.; Grimm, R. (2006), "Evidence for Efimov quantum states in an ultracold gas of caesium atoms", Nature, 440 (7082): 315–318, arXiv:cond-mat/0512394, Bibcode:2006Natur.440..315K, doi:10.1038/nature04626, PMID 16541068, S2CID 4379828
Tanaka, K. (2010), "Observation of a Large Reaction Cross Section in the Drip-Line Nucleus ²²C", Physical Review Letters, 104 (6): 062701, Bibcode:2010PhRvL.104f2701T, doi:10.1103/PhysRevLett.104.062701, PMID 20366816, S2CID 7951719

jasoncantarella.com

Cantarella, Jason; Fu, Joseph H. G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C. (2006), "Criticality for the Gehring link problem" (PDF), Geometry & Topology, 10 (4): 2055–2116, arXiv:math/0402212, doi:10.2140/gt.2006.10.2055, MR 2284052
Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891

jstor.org

Schoeck, Richard J. (Spring 1968), "Mathematics and the languages of literary criticism", The Journal of Aesthetics and Art Criticism, 26 (3): 367–376, doi:10.2307/429121, JSTOR 429121
Saiber, Arielle; Mbirika, aBa (2013), "The Three Giri of Paradiso 33" (PDF), Dante Studies (131): 237–272, JSTOR 43490498
Baird, Joseph L. (1970), "Unferth the þyle", Medium Ævum, 39 (1): 1–12, doi:10.2307/43631234, JSTOR 43631234, the stone bears also representations of three horns interlaced
Nanyes, Ollie (October 1993), "An elementary proof that the Borromean rings are non-splittable", American Mathematical Monthly, 100 (8): 786–789, doi:10.2307/2324788, JSTOR 2324788
Lindström, Bernt; Zetterström, Hans-Olov (1991), "Borromean circles are impossible", American Mathematical Monthly, 98 (4): 340–341, doi:10.2307/2323803, JSTOR 2323803. Note however that Gunn & Sullivan (2008) write that this reference "seems to incorrectly deal only with the case that the three-dimensional configuration has a projection homeomorphic to" the conventional three-circle drawing of the link.
Burgiel, H.; Franzblau, D. S.; Gutschera, K. R. (1996), "The mystery of the linked triangles", Mathematics Magazine, 69 (2): 94–102, doi:10.1080/0025570x.1996.11996399, JSTOR 2690662, MR 1394792
Abbott, Steve (July 1997), "Review of Not Knot and Supplement to Not Knot", The Mathematical Gazette, 81 (491): 340–342, doi:10.2307/3619248, JSTOR 3619248, S2CID 64589738

katlas.org

"Borromean rings", The Knot Atlas.

livescience.com

Moskowitz, Clara (December 16, 2009), "Strange physical theory proved after nearly 40 years", Live Science

msri.org

library.msri.org

William Thurston (March 2002), "7. Computation of volume", The Geometry and Topology of Three-Manifolds, p. 165, archived from the original (PDF) on 2020-07-27, retrieved 2012-01-17

nih.gov

pubmed.ncbi.nlm.nih.gov

Bruns, Carson J.; Stoddart, J. Fraser (2011), "The mechanical bond: A work of art", in Fabbrizzi, L. (ed.), Beauty in Chemistry, Topics in Current Chemistry, vol. 323, Springer, pp. 19–72, doi:10.1007/128_2011_296, PMID 22183145
Chichak, Kelly S.; Cantrill, Stuart J.; Pease, Anthony R.; Chiu, Sheng-Hsien; Cave, Gareth W. V.; Atwood, Jerry L.; Stoddart, J. Fraser (May 28, 2004), "Molecular Borromean rings" (PDF), Science, 304 (5675): 1308–1312, Bibcode:2004Sci...304.1308C, doi:10.1126/science.1096914, PMID 15166376, S2CID 45191675
Mao, C.; Sun, W.; Seeman, N. C. (1997), "Assembly of Borromean rings from DNA", Nature, 386 (6621): 137–138, Bibcode:1997Natur.386..137M, doi:10.1038/386137b0, PMID 9062186, S2CID 4321733
Kumar, Vijith; Pilati, Tullio; Terraneo, Giancarlo; Meyer, Franck; Metrangolo, Pierangelo; Resnati, Giuseppe (2017), "Halogen bonded Borromean networks by design: topology invariance and metric tuning in a library of multi-component systems", Chemical Science, 8 (3): 1801–1810, doi:10.1039/C6SC04478F, PMC 5477818, PMID 28694953
Kraemer, T.; Mark, M.; Waldburger, P.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Nägerl, H.-C.; Grimm, R. (2006), "Evidence for Efimov quantum states in an ultracold gas of caesium atoms", Nature, 440 (7082): 315–318, arXiv:cond-mat/0512394, Bibcode:2006Natur.440..315K, doi:10.1038/nature04626, PMID 16541068, S2CID 4379828
Tanaka, K. (2010), "Observation of a Large Reaction Cross Section in the Drip-Line Nucleus ²²C", Physical Review Letters, 104 (6): 062701, Bibcode:2010PhRvL.104f2701T, doi:10.1103/PhysRevLett.104.062701, PMID 20366816, S2CID 7951719

ncbi.nlm.nih.gov

Kumar, Vijith; Pilati, Tullio; Terraneo, Giancarlo; Meyer, Franck; Metrangolo, Pierangelo; Resnati, Giuseppe (2017), "Halogen bonded Borromean networks by design: topology invariance and metric tuning in a library of multi-component systems", Chemical Science, 8 (3): 1801–1810, doi:10.1039/C6SC04478F, PMC 5477818, PMID 28694953

ntu.ac.uk

irep.ntu.ac.uk

Chichak, Kelly S.; Cantrill, Stuart J.; Pease, Anthony R.; Chiu, Sheng-Hsien; Cave, Gareth W. V.; Atwood, Jerry L.; Stoddart, J. Fraser (May 28, 2004), "Molecular Borromean rings" (PDF), Science, 304 (5675): 1308–1312, Bibcode:2004Sci...304.1308C, doi:10.1126/science.1096914, PMID 15166376, S2CID 45191675

popmath.org.uk

"African Borromean Rings", Mathematics and Knots, Centre for the Popularisation of Maths, University of Wales, 2002, retrieved 2021-02-12

projecteuclid.org

Thistlethwaite, Morwen B. (1991), "On the algebraic part of an alternating link", Pacific Journal of Mathematics, 151 (2): 317–333, doi:10.2140/pjm.1991.151.317, MR 1132393

researchgate.net

Freeman, Jim (2015), "Gathering clues from Margot's extraordinary objects", Tewkesbury Historical Society Bulletin, 24

scientificamerican.com

Gardner, Martin (September 1961), "Surfaces with edges linked in the same way as the three rings of a well-known design", Mathematical Games, Scientific American, reprinted as Gardner, Martin (1991), "Knots and Borromean Rings", The Unexpected Hanging and Other Mathematical Diversions, University of Chicago Press, pp. 24–33; see also Gardner, Martin (September 1978), "The Toroids of Dr. Klonefake", Asimov's Science Fiction, vol. 2, no. 5, p. 29

semanticscholar.org

api.semanticscholar.org

Cromwell, Peter; Beltrami, Elisabetta; Rampichini, Marta (March 1998), "The Borromean rings", The mathematical tourist, The Mathematical Intelligencer, 20 (1): 53–62, doi:10.1007/bf03024401, S2CID 189888135
Chamberland, Marc; Herman, Eugene A. (2015), "Rock-paper-scissors meets Borromean rings", The Mathematical Intelligencer, 37 (2): 20–25, doi:10.1007/s00283-014-9499-4, MR 3356112, S2CID 558993
Lakshminarayan, Arul (May 2007), "Borromean triangles and prime knots in an ancient temple", Resonance, 12 (5): 41–47, doi:10.1007/s12045-007-0049-7, S2CID 120259064
Glick, Ned (September 1999), "The 3-ring symbol of Ballantine Beer", The mathematical tourist, The Mathematical Intelligencer, 21 (4): 15–16, doi:10.1007/bf03025332, S2CID 123311380
Bai, Sheng; Wang, Weibiao (2020), "New criteria and constructions of Brunnian links", Journal of Knot Theory and Its Ramifications, 29 (13): 2043008, 27, arXiv:2006.10290, doi:10.1142/S0218216520430087, MR 4213076, S2CID 219792382
Howards, Hugh Nelson (2013), "Forming the Borromean rings out of arbitrary polygonal unknots", Journal of Knot Theory and Its Ramifications, 22 (14): 1350083, 15, arXiv:1406.3370, doi:10.1142/S0218216513500831, MR 3190121, S2CID 119674622
Cantarella, Jason; Kusner, Robert B.; Sullivan, John M. (2002), "On the minimum ropelength of knots and links" (PDF), Inventiones Mathematicae, 150 (2): 257–286, arXiv:math/0103224, Bibcode:2002InMat.150..257C, doi:10.1007/s00222-002-0234-y, MR 1933586, S2CID 730891
Abbott, Steve (July 1997), "Review of Not Knot and Supplement to Not Knot", The Mathematical Gazette, 81 (491): 340–342, doi:10.2307/3619248, JSTOR 3619248, S2CID 64589738
Chichak, Kelly S.; Cantrill, Stuart J.; Pease, Anthony R.; Chiu, Sheng-Hsien; Cave, Gareth W. V.; Atwood, Jerry L.; Stoddart, J. Fraser (May 28, 2004), "Molecular Borromean rings" (PDF), Science, 304 (5675): 1308–1312, Bibcode:2004Sci...304.1308C, doi:10.1126/science.1096914, PMID 15166376, S2CID 45191675
Mao, C.; Sun, W.; Seeman, N. C. (1997), "Assembly of Borromean rings from DNA", Nature, 386 (6621): 137–138, Bibcode:1997Natur.386..137M, doi:10.1038/386137b0, PMID 9062186, S2CID 4321733
Kraemer, T.; Mark, M.; Waldburger, P.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Nägerl, H.-C.; Grimm, R. (2006), "Evidence for Efimov quantum states in an ultracold gas of caesium atoms", Nature, 440 (7082): 315–318, arXiv:cond-mat/0512394, Bibcode:2006Natur.440..315K, doi:10.1038/nature04626, PMID 16541068, S2CID 4379828
Tanaka, K. (2010), "Observation of a Large Reaction Cross Section in the Drip-Line Nucleus ²²C", Physical Review Letters, 104 (6): 062701, Bibcode:2010PhRvL.104f2701T, doi:10.1103/PhysRevLett.104.062701, PMID 20366816, S2CID 7951719

tripod.com

members.tripod.com

Jablan, Slavik V. (1999), "Are Borromean links so rare?", Proceedings of the 2nd International Katachi U Symmetry Symposium, Part 1 (Tsukuba, 1999), Forma, 14 (4): 269–277, MR 1770213

uiuc.edu

torus.math.uiuc.edu

Gunn, Charles; Sullivan, John M. (2008), "The Borromean Rings: A video about the New IMU logo", in Sarhangi, Reza; Séquin, Carlo H. (eds.), Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, London: Tarquin Publications, pp. 63–70, ISBN 978-0-9665201-9-4; see the video itself at "The Borromean Rings: A new logo for the IMU Archived 2021-03-08 at the Wayback Machine" [w/video], International Mathematical Union

uni-heidelberg.de

ub.uni-heidelberg.de

Vogel, Denis (2005), Masseyprodukte in der Galoiskohomologie von Zahlkörpern [Massey products in the Galois cohomology of number fields], Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005, Göttingen: Universitätsdrucke Göttingen, pp. 93–98, doi:10.11588/heidok.00004418, MR 2206880

uwec.edu

people.uwec.edu

Saiber, Arielle; Mbirika, aBa (2013), "The Three Giri of Paradiso 33" (PDF), Dante Studies (131): 237–272, JSTOR 43490498

web.archive.org

Gunn, Charles; Sullivan, John M. (2008), "The Borromean Rings: A video about the New IMU logo", in Sarhangi, Reza; Séquin, Carlo H. (eds.), Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, London: Tarquin Publications, pp. 63–70, ISBN 978-0-9665201-9-4; see the video itself at "The Borromean Rings: A new logo for the IMU Archived 2021-03-08 at the Wayback Machine" [w/video], International Mathematical Union
Tverberg, Helge (2010), "On Borromean rings" (PDF), The Mathematical Scientist, 35 (1): 57–60, MR 2668444, archived from the original (PDF) on 2021-03-16, retrieved 2021-03-16
William Thurston (March 2002), "7. Computation of volume", The Geometry and Topology of Three-Manifolds, p. 165, archived from the original (PDF) on 2020-07-27, retrieved 2012-01-17

worldcat.org

search.worldcat.org

Natarajan, Ganapati; Mathew, Ammu; Negishi, Yuichi; Whetten, Robert L.; Pradeep, Thalappil (2015-12-02), "A unified framework for understanding the structure and modifications of atomically precise monolayer protected gold clusters", The Journal of Physical Chemistry C, 119 (49): 27768–27785, doi:10.1021/acs.jpcc.5b08193, ISSN 1932-7447

wpi.edu

users.wpi.edu

Aravind, P. K. (1997), "Borromean entanglement of the GHZ state" (PDF), in Cohen, R. S.; Horne, M.; Stachel, J. (eds.), Potentiality, Entanglement and Passion-at-a-Distance, Boston Studies in the Philosophy of Science, Springer, pp. 53–59, doi:10.1007/978-94-017-2732-7_4, MR 1739812