Tessellation (English Wikipedia)

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

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Robinson, Raphael M. (1971). "Undecidability and nonperiodicity for tilings of the plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/bf01418780. MR 0297572. S2CID 14259496.
Culik, Karel II (1996). "An aperiodic set of 13 Wang tiles". Discrete Mathematics. 160 (1–3): 245–251. doi:10.1016/S0012-365X(96)00118-5. MR 1417576.
Engel, Peter (1981). "Über Wirkungsbereichsteilungen von kubischer Symmetrie". Zeitschrift für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie. 154 (3–4): 199–215. Bibcode:1981ZK....154..199E. doi:10.1524/zkri.1981.154.3-4.199. MR 0598811..

ams.org

Grünbaum, Branko (June–July 2006). "What symmetry groups are present in the Alhambra?" (PDF). Notices of the American Mathematical Society. 53 (6): 670–673.
Austin, David. "Penrose Tiles Talk Across Miles". American Mathematical Society. Retrieved 29 May 2015.

archive.org

Gullberg 1997, p. 395. Gullberg, Jan (1997). Mathematics From the Birth of Numbers. Norton. ISBN 978-0-393-04002-9.
Escher 1974, pp. 11–12, 15–16. Escher, M. C. (1974). J. L. Locher (ed.). The World of M. C. Escher (New Concise NAL ed.). Abrams. ISBN 978-0-451-79961-6.
Grünbaum & Shephard 1987, p. 59. Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman. ISBN 978-0-7167-1193-3.
Wells, David (1991). "two squares tessellation". The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin Books. pp. 260–261. ISBN 978-0-14-011813-1.
Armstrong, M.A. (1988). Groups and Symmetry. New York: Springer-Verlag. ISBN 978-3-540-96675-3.
Oldershaw, Cally (2003). Firefly Guide to Gems. Firefly Books. p. 107. ISBN 978-1-55297-814-6.
Coxeter, Harold Scott Macdonald; Sherk, F. Arthur; Canadian Mathematical Society (1995). Kaleidoscopes: Selected Writings of H.S.M. Coxeter. John Wiley & Sons. p. 3 and passim. ISBN 978-0-471-01003-6.
Escher 1974, pp. 5, 17. Escher, M. C. (1974). J. L. Locher (ed.). The World of M. C. Escher (New Concise NAL ed.). Abrams. ISBN 978-0-451-79961-6.
Escher 1974, pp. 142–143. Escher, M. C. (1974). J. L. Locher (ed.). The World of M. C. Escher (New Concise NAL ed.). Abrams. ISBN 978-0-451-79961-6.
Escher 1974, p. 16. Escher, M. C. (1974). J. L. Locher (ed.). The World of M. C. Escher (New Concise NAL ed.). Abrams. ISBN 978-0-451-79961-6.
Martin, George E. (1991). Polyominoes: A guide to puzzles and problems in tiling. Mathematical Association of America. ISBN 978-0-88385-501-0.
Frederickson, Greg N. (2002). Hinged Dissections: Swinging and Twisting. Cambridge University Press. ISBN 978-0-521-81192-7.

arxiv.org

Margenstern, Maurice (4 January 2011). "Coordinates for a new triangular tiling of the hyperbolic plane". arXiv:1101.0530 [cs.FL].
Schreiber, Tomasz; Soja, Natalia (2010). "Limit theory for planar Gilbert tessellations". arXiv:1005.0023 [math.PR].

basilicasanmarco.it

"Basilica di San Marco". Section: Tessellated floor. Basilica di San Marco. Retrieved 26 April 2013.

books.google.com

Shubnikov, Alekseĭ Vasilʹevich; Belov, Nikolaĭ Vasilʹevich (1964). Colored Symmetry. Macmillan.
Coxeter, H. S. M. (1948). Regular Polytopes. Methuen. pp. 14, 69, 149. ISBN 978-0-486-61480-9.
Emmer, Michele; Schattschneider, Doris (8 May 2007). M.C. Escher's Legacy: A Centennial Celebration. Berlin Heidelberg: Springer. p. 325. ISBN 978-3-540-28849-7.
Senechal, Marjorie (26 September 1996). Quasicrystals and Geometry. CUP Archive. p. 209. ISBN 978-0-521-57541-6.
Whittaker, Andrew (2008). Speak the Culture: Spain. Thorogood Publishing. p. 153. ISBN 978-1-85418-605-8.
Gardner, Martin (14 December 2006). Aha! A Two Volume Collection: Aha! Gotcha Aha! Insight. MAA. p. 48. ISBN 978-0-88385-551-5.

doi.org

Schattschneider, Doris (September 1980). "Will It Tile? Try the Conway Criterion!". Mathematics Magazine. Vol. 53, no. 4. pp. 224–233. doi:10.2307/2689617. JSTOR 2689617.
Hirschhorn, M. D.; Hunt, D. C. (1985). "Equilateral convex pentagons which tile the plane". Journal of Combinatorial Theory. Series A. 39 (1): 1–18. doi:10.1016/0097-3165(85)90078-0.
Kirby, Matthew; Umble, Ronald (2011). "Edge Tessellations and Stamp Folding Puzzles". Mathematics Magazine. 84 (4): 283–89. doi:10.4169/math.mag.84.4.283. S2CID 123579388.
Lu, Peter J.; Steinhardt (23 February 2007). "Decagonal and quasi-crystalline tilings in medieval Islamic architecture". Science. 315 (5815): 1106–10. Bibcode:2007Sci...315.1106L. doi:10.1126/science.1135491. PMID 17322056. S2CID 10374218.
Radin, C. (May 1994). "The Pinwheel Tilings of the Plane". Annals of Mathematics. 139 (3): 661–702. CiteSeerX 10.1.1.44.9723. doi:10.2307/2118575. JSTOR 2118575.
Dharma-wardana, M. W. C.; MacDonald, A. H.; Lockwood, D. J.; Baribeau, J.-M.; Houghton, D. C. (1987). "Raman scattering in Fibonacci superlattices". Physical Review Letters. 58 (17): 1761–1765. Bibcode:1987PhRvL..58.1761D. doi:10.1103/physrevlett.58.1761. PMID 10034529.
Wang, Hao (1961). "Proving theorems by pattern recognition—II". Bell System Technical Journal. 40 (1): 1–41. doi:10.1002/j.1538-7305.1961.tb03975.x.
Berger, Robert (1966). "The undecidability of the domino problem". Memoirs of the American Mathematical Society. 66 (66): 72. doi:10.1090/memo/0066.
Robinson, Raphael M. (1971). "Undecidability and nonperiodicity for tilings of the plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/bf01418780. MR 0297572. S2CID 14259496.
Culik, Karel II (1996). "An aperiodic set of 13 Wang tiles". Discrete Mathematics. 160 (1–3): 245–251. doi:10.1016/S0012-365X(96)00118-5. MR 1417576.
Browne, Cameron (2008). "Truchet curves and surfaces". Computers & Graphics. 32 (2): 268–281. doi:10.1016/j.cag.2007.10.001.
Smith, Cyril Stanley (1987). "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy". Leonardo. 20 (4): 373–385. doi:10.2307/1578535. JSTOR 1578535. S2CID 192944820.
Aurenhammer, Franz (1991). "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure". ACM Computing Surveys. 23 (3): 345–405. doi:10.1145/116873.116880. S2CID 4613674.
Engel, Peter (1981). "Über Wirkungsbereichsteilungen von kubischer Symmetrie". Zeitschrift für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie. 154 (3–4): 199–215. Bibcode:1981ZK....154..199E. doi:10.1524/zkri.1981.154.3-4.199. MR 0598811..
Schwarz, H. A. (1873). "Ueber diejenigen Fälle in welchen die Gaussichen hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt". Journal für die reine und angewandte Mathematik. 1873 (75): 292–335. doi:10.1515/crll.1873.75.292. ISSN 0075-4102. S2CID 121698536.
Thouless, M. D. (1990). "Crack Spacing in Brittle Films on Elastic Substrates". J. Am. Chem. Soc. 73 (7): 2144–2146. doi:10.1111/j.1151-2916.1990.tb05290.x.
Xia, Z. C.; Hutchinson, J. W. (2000). "Crack patterns in thin films". J. Mech. Phys. Solids. 48 (6–7): 1107–1131. Bibcode:2000JMPSo..48.1107X. doi:10.1016/S0022-5096(99)00081-2.
Seghir, R.; Arscott, S. (2015). "Controlled mud-crack patterning and self-organized cracking of polydimethylsiloxane elastomer surfaces". Sci. Rep. 5: 14787. Bibcode:2015NatSR...514787S. doi:10.1038/srep14787. PMC 4594096. PMID 26437880.
Ball, Philip (2013). "How honeycombs can build themselves". Nature. doi:10.1038/nature.2013.13398. S2CID 138195687. Retrieved 7 November 2014.
Gray, N. H.; Anderson, J. B.; Devine, J. D.; Kwasnik, J. M. (1976). "Topological properties of random crack networks". Mathematical Geology. 8 (6): 617–626. doi:10.1007/BF01031092. S2CID 119949515.
Weaire, D.; Rivier, N. (1984). "Soap, cells and statistics: Random patterns in two dimensions". Contemporary Physics. 25 (1): 59–99. Bibcode:1984ConPh..25...59W. doi:10.1080/00107518408210979.
Schattschneider, Doris (1978). "Tiling the Plane with Congruent Pentagons" (PDF). Mathematics Magazine. 51 (1). MAA: 29–44. doi:10.2307/2689644. JSTOR 2689644.
Henle, Frederick V.; Henle, James M. (2008). "Squaring the plane" (PDF). American Mathematical Monthly. 115 (1): 3–12. doi:10.1080/00029890.2008.11920491. JSTOR 27642387. S2CID 26663945. Archived from the original (PDF) on 20 June 2006.

encyclopediaofmath.org

"Four-colour problem", Encyclopedia of Mathematics, EMS Press, 2001 [1994]

harvard.edu

ui.adsabs.harvard.edu

Lu, Peter J.; Steinhardt (23 February 2007). "Decagonal and quasi-crystalline tilings in medieval Islamic architecture". Science. 315 (5815): 1106–10. Bibcode:2007Sci...315.1106L. doi:10.1126/science.1135491. PMID 17322056. S2CID 10374218.
Dharma-wardana, M. W. C.; MacDonald, A. H.; Lockwood, D. J.; Baribeau, J.-M.; Houghton, D. C. (1987). "Raman scattering in Fibonacci superlattices". Physical Review Letters. 58 (17): 1761–1765. Bibcode:1987PhRvL..58.1761D. doi:10.1103/physrevlett.58.1761. PMID 10034529.
Robinson, Raphael M. (1971). "Undecidability and nonperiodicity for tilings of the plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/bf01418780. MR 0297572. S2CID 14259496.
Engel, Peter (1981). "Über Wirkungsbereichsteilungen von kubischer Symmetrie". Zeitschrift für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie. 154 (3–4): 199–215. Bibcode:1981ZK....154..199E. doi:10.1524/zkri.1981.154.3-4.199. MR 0598811..
Xia, Z. C.; Hutchinson, J. W. (2000). "Crack patterns in thin films". J. Mech. Phys. Solids. 48 (6–7): 1107–1131. Bibcode:2000JMPSo..48.1107X. doi:10.1016/S0022-5096(99)00081-2.
Seghir, R.; Arscott, S. (2015). "Controlled mud-crack patterning and self-organized cracking of polydimethylsiloxane elastomer surfaces". Sci. Rep. 5: 14787. Bibcode:2015NatSR...514787S. doi:10.1038/srep14787. PMC 4594096. PMID 26437880.
Weaire, D.; Rivier, N. (1984). "Soap, cells and statistics: Random patterns in two dimensions". Contemporary Physics. 25 (1): 59–99. Bibcode:1984ConPh..25...59W. doi:10.1080/00107518408210979.

hullcc.gov.uk

"The Brantingham Geometric Mosaics". Hull City Council. 2008. Retrieved 26 May 2015.

jigsaw-puzzle.org

McAdam, Daniel. "History of Jigsaw Puzzles". American Jigsaw Puzzle Society. Archived from the original on 11 February 2014. Retrieved 28 May 2015.

josleys.com

Leys, Jos (2015). "Hyperbolic Escher". Retrieved 27 May 2015.

jstor.org

Schattschneider, Doris (September 1980). "Will It Tile? Try the Conway Criterion!". Mathematics Magazine. Vol. 53, no. 4. pp. 224–233. doi:10.2307/2689617. JSTOR 2689617.
Radin, C. (May 1994). "The Pinwheel Tilings of the Plane". Annals of Mathematics. 139 (3): 661–702. CiteSeerX 10.1.1.44.9723. doi:10.2307/2118575. JSTOR 2118575.
Smith, Cyril Stanley (1987). "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy". Leonardo. 20 (4): 373–385. doi:10.2307/1578535. JSTOR 1578535. S2CID 192944820.
Schattschneider, Doris (1978). "Tiling the Plane with Congruent Pentagons" (PDF). Mathematics Magazine. 51 (1). MAA: 29–44. doi:10.2307/2689644. JSTOR 2689644.
Henle, Frederick V.; Henle, James M. (2008). "Squaring the plane" (PDF). American Mathematical Monthly. 115 (1): 3–12. doi:10.1080/00029890.2008.11920491. JSTOR 27642387. S2CID 26663945. Archived from the original (PDF) on 20 June 2006.

lanl.gov

public.lanl.gov

Djidjev, Hristo; Potkonjak, Miodrag (2012). "Dynamic Coverage Problems in Sensor Networks" (PDF). Los Alamos National Laboratory. p. 2. Retrieved 6 April 2013.

m-w.com

"Tessellate". Merriam-Webster Online. Retrieved 26 May 2015.

maa.org

Schattschneider, Doris (1978). "Tiling the Plane with Congruent Pentagons" (PDF). Mathematics Magazine. 51 (1). MAA: 29–44. doi:10.2307/2689644. JSTOR 2689644.

mathematicians.org.uk

Harriss, E. O. "Aperiodic Tiling" (PDF). University of London and EPSRC. Archived from the original (PDF) on 29 August 2017. Retrieved 29 May 2015.

maths.org

nrich.maths.org

NRICH (Millennium Maths Project) (1997–2012). "Schläfli Tessellations". University of Cambridge. Retrieved 26 April 2013.

nature.com

Ball, Philip (2013). "How honeycombs can build themselves". Nature. doi:10.1038/nature.2013.13398. S2CID 138195687. Retrieved 7 November 2014.

nih.gov

pubmed.ncbi.nlm.nih.gov

Lu, Peter J.; Steinhardt (23 February 2007). "Decagonal and quasi-crystalline tilings in medieval Islamic architecture". Science. 315 (5815): 1106–10. Bibcode:2007Sci...315.1106L. doi:10.1126/science.1135491. PMID 17322056. S2CID 10374218.
Dharma-wardana, M. W. C.; MacDonald, A. H.; Lockwood, D. J.; Baribeau, J.-M.; Houghton, D. C. (1987). "Raman scattering in Fibonacci superlattices". Physical Review Letters. 58 (17): 1761–1765. Bibcode:1987PhRvL..58.1761D. doi:10.1103/physrevlett.58.1761. PMID 10034529.
Seghir, R.; Arscott, S. (2015). "Controlled mud-crack patterning and self-organized cracking of polydimethylsiloxane elastomer surfaces". Sci. Rep. 5: 14787. Bibcode:2015NatSR...514787S. doi:10.1038/srep14787. PMC 4594096. PMID 26437880.

ncbi.nlm.nih.gov

Seghir, R.; Arscott, S. (2015). "Controlled mud-crack patterning and self-organized cracking of polydimethylsiloxane elastomer surfaces". Sci. Rep. 5: 14787. Bibcode:2015NatSR...514787S. doi:10.1038/srep14787. PMC 4594096. PMID 26437880.

nus.edu.sg

math.nus.edu.sg

"Mathematics in Art and Architecture". National University of Singapore. Retrieved 17 May 2015.

nytimes.com

Roberts, Soibhan, Elusive 'Einstein' Solves a Longstanding Mathematical Problem, the New York Times, March 28, 2023, with image of the pattern
Suri, Mani (12 October 2015). "The Importance of Recreational Math". New York Times.

psu.edu

citeseerx.ist.psu.edu

Huson, Daniel H. (1991). "Two-Dimensional Symmetry Mutation". Princeton University. CiteSeerX 10.1.1.30.8536 – via CiteSeerX.
Radin, C. (May 1994). "The Pinwheel Tilings of the Plane". Annals of Mathematics. 139 (3): 661–702. CiteSeerX 10.1.1.44.9723. doi:10.2307/2118575. JSTOR 2118575.

sciencenews.org

Conover, Emily (24 March 2023). "Mathematicians have finally discovered an elusive 'einstein' tile". Science News. Retrieved 25 March 2023. with image of the pattern

semanticscholar.org

api.semanticscholar.org

Kirby, Matthew; Umble, Ronald (2011). "Edge Tessellations and Stamp Folding Puzzles". Mathematics Magazine. 84 (4): 283–89. doi:10.4169/math.mag.84.4.283. S2CID 123579388.
Lu, Peter J.; Steinhardt (23 February 2007). "Decagonal and quasi-crystalline tilings in medieval Islamic architecture". Science. 315 (5815): 1106–10. Bibcode:2007Sci...315.1106L. doi:10.1126/science.1135491. PMID 17322056. S2CID 10374218.
Robinson, Raphael M. (1971). "Undecidability and nonperiodicity for tilings of the plane". Inventiones Mathematicae. 12 (3): 177–209. Bibcode:1971InMat..12..177R. doi:10.1007/bf01418780. MR 0297572. S2CID 14259496.
Smith, Cyril Stanley (1987). "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy". Leonardo. 20 (4): 373–385. doi:10.2307/1578535. JSTOR 1578535. S2CID 192944820.
Aurenhammer, Franz (1991). "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure". ACM Computing Surveys. 23 (3): 345–405. doi:10.1145/116873.116880. S2CID 4613674.
Schwarz, H. A. (1873). "Ueber diejenigen Fälle in welchen die Gaussichen hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt". Journal für die reine und angewandte Mathematik. 1873 (75): 292–335. doi:10.1515/crll.1873.75.292. ISSN 0075-4102. S2CID 121698536.
Ball, Philip (2013). "How honeycombs can build themselves". Nature. doi:10.1038/nature.2013.13398. S2CID 138195687. Retrieved 7 November 2014.
Gray, N. H.; Anderson, J. B.; Devine, J. D.; Kwasnik, J. M. (1976). "Topological properties of random crack networks". Mathematical Geology. 8 (6): 617–626. doi:10.1007/BF01031092. S2CID 119949515.
Henle, Frederick V.; Henle, James M. (2008). "Squaring the plane" (PDF). American Mathematical Monthly. 115 (1): 3–12. doi:10.1080/00029890.2008.11920491. JSTOR 27642387. S2CID 26663945. Archived from the original (PDF) on 20 June 2006.

smith.edu

maven.smith.edu

Henle, Frederick V.; Henle, James M. (2008). "Squaring the plane" (PDF). American Mathematical Monthly. 115 (1): 3–12. doi:10.1080/00029890.2008.11920491. JSTOR 27642387. S2CID 26663945. Archived from the original (PDF) on 20 June 2006.

springer.com

Moller, Jesper (1994). Lectures on Random Voronoi Tessellations. Springer. ISBN 978-1-4612-2652-9.

squaring.net

Tutte, W. T. "Squaring the Square". Squaring.net. Retrieved 29 May 2015.

uni-goettingen.de

resolver.sub.uni-goettingen.de

Schwarz, H. A. (1873). "Ueber diejenigen Fälle in welchen die Gaussichen hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt". Journal für die reine und angewandte Mathematik. 1873 (75): 292–335. doi:10.1515/crll.1873.75.292. ISSN 0075-4102. S2CID 121698536.

utah.edu

math.utah.edu

Gersten, S. M. "Introduction to Hyperbolic and Automatic Groups" (PDF). University of Utah. Retrieved 27 May 2015. Figure 1 is part of a tiling of the Euclidean plane, which we imagine as continued in all directions, and Figure 2 [Circle Limit IV] is a beautiful tesselation of the Poincaré unit disc model of the hyperbolic plane by white tiles representing angels and black tiles representing devils. An important feature of the second is that all white tiles are mutually congruent as are all black tiles; of course this is not true for the Euclidean metric, but holds for the Poincaré metric

uwgb.edu

Dutch, Steven (29 July 1999). "Some Special Radial and Spiral Tilings". University of Wisconsin. Archived from the original on 4 April 2013. Retrieved 6 April 2013.

web.archive.org

Dutch, Steven (29 July 1999). "Some Special Radial and Spiral Tilings". University of Wisconsin. Archived from the original on 4 April 2013. Retrieved 6 April 2013.
Harriss, E. O. "Aperiodic Tiling" (PDF). University of London and EPSRC. Archived from the original (PDF) on 29 August 2017. Retrieved 29 May 2015.
"Reducing yield losses: using less metal to make the same thing". UIT Cambridge. Archived from the original on 29 May 2015. Retrieved 29 May 2015.
McAdam, Daniel. "History of Jigsaw Puzzles". American Jigsaw Puzzle Society. Archived from the original on 11 February 2014. Retrieved 28 May 2015.
Henle, Frederick V.; Henle, James M. (2008). "Squaring the plane" (PDF). American Mathematical Monthly. 115 (1): 3–12. doi:10.1080/00029890.2008.11920491. JSTOR 27642387. S2CID 26663945. Archived from the original (PDF) on 20 June 2006.