Pentagonal tiling (English Wikipedia)

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

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11doi.org

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7ams.org

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ams.org

mathscinet.ams.org

Grünbaum & Shephard 1987, Sec. 9.3 Other Monohedral tilings by convex polygons. Grünbaum, Branko; Shephard, Geoffrey C. (1987), "Tilings by polygons", Tilings and Patterns, New York: W. H. Freeman and Company, ISBN 978-0-7167-1193-3, MR 0857454
Schattschneider 1978. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Schattschneider 1978, Fig 12. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Hirschhorn & Hunt 1985. Hirschhorn, M. D.; Hunt, D. C. (1985), "Equilateral convex pentagons which tile the plane" (PDF), Journal of Combinatorial Theory, Series A, 39 (1): 1–18, doi:10.1016/0097-3165(85)90078-0, ISSN 1096-0899, MR 0787713, retrieved 2020-10-30
Godrèche 1989. Godrèche, C. (1989), "The sphinx: a limit-periodic tiling of the plane", Journal of Physics A: Mathematical and General, 22 (24): L1163 – L1166, Bibcode:1989JPhA...22L1163G, doi:10.1088/0305-4470/22/24/006, MR 1030678
Frettlöh, Dirk; Garber, Alexey (2015), "Symmetries of monocoronal tilings", Discrete Mathematics & Theoretical Computer Science, 17 (2): 203–234, arXiv:1402.4658, doi:10.46298/dmtcs.2142, MR 3411398

ams.org

Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Nirlee; Vieira, Luis Sordo; Wikner, Elena (2012-05-01), "Isoperimetric Pentagonal Tilings", Notices of the American Mathematical Society, 59 (5): 632, doi:10.1090/noti838, ISSN 0002-9920

archive.org

Grünbaum & Shephard 1987, Sec. 9.3 Other Monohedral tilings by convex polygons. Grünbaum, Branko; Shephard, Geoffrey C. (1987), "Tilings by polygons", Tilings and Patterns, New York: W. H. Freeman and Company, ISBN 978-0-7167-1193-3, MR 0857454

arxiv.org

Rao 2017. Rao, Michaël (2017), Exhaustive search of convex pentagons which tile the plane (PDF), arXiv:1708.00274
Mann, McLoud-Mann & Von Derau 2018. Mann, Casey; McLoud-Mann, Jennifer; Von Derau, David (2018), "Convex pentagons that admit $i$ -block transitive tilings", Geometriae Dedicata, 194 (1): 141–167, arXiv:1510.01186, doi:10.1007/s10711-017-0270-9, S2CID 119176351
Klaassen 2016. Klaassen, Bernhard (2016), "Rotationally symmetric tilings with convex pentagons and hexagons", Elemente der Mathematik, 71 (4): 137–144, arXiv:1509.06297, doi:10.4171/em/310, ISSN 0013-6018, S2CID 119738738
Frettlöh, Dirk; Garber, Alexey (2015), "Symmetries of monocoronal tilings", Discrete Mathematics & Theoretical Computer Science, 17 (2): 203–234, arXiv:1402.4658, doi:10.46298/dmtcs.2142, MR 3411398

beloit.edu

Chavey 1989. Chavey, D. (1989), "Tilings by Regular Polygons—II: A Catalog of Tilings", Computers & Mathematics with Applications, 17 (1–3): 147–165, doi:10.1016/0898-1221(89)90156-9

core.ac.uk

Hirschhorn & Hunt 1985. Hirschhorn, M. D.; Hunt, D. C. (1985), "Equilateral convex pentagons which tile the plane" (PDF), Journal of Combinatorial Theory, Series A, 39 (1): 1–18, doi:10.1016/0097-3165(85)90078-0, ISSN 1096-0899, MR 0787713, retrieved 2020-10-30

doi.org

Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Nirlee; Vieira, Luis Sordo; Wikner, Elena (2012-05-01), "Isoperimetric Pentagonal Tilings", Notices of the American Mathematical Society, 59 (5): 632, doi:10.1090/noti838, ISSN 0002-9920
Grünbaum & Shephard 1978. Grünbaum, Branko; Shephard, Geoffrey C. (1978), "Isohedral tilings of the plane by polygons", Commentarii Mathematici Helvetici, 53: 542–571, doi:10.1007/bf02566098, ISSN 0010-2571, S2CID 119897404
Schattschneider 1978. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Mann, McLoud-Mann & Von Derau 2018. Mann, Casey; McLoud-Mann, Jennifer; Von Derau, David (2018), "Convex pentagons that admit $i$ -block transitive tilings", Geometriae Dedicata, 194 (1): 141–167, arXiv:1510.01186, doi:10.1007/s10711-017-0270-9, S2CID 119176351
Schattschneider 1978, Fig 12. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Hirschhorn & Hunt 1985. Hirschhorn, M. D.; Hunt, D. C. (1985), "Equilateral convex pentagons which tile the plane" (PDF), Journal of Combinatorial Theory, Series A, 39 (1): 1–18, doi:10.1016/0097-3165(85)90078-0, ISSN 1096-0899, MR 0787713, retrieved 2020-10-30
Klaassen 2016. Klaassen, Bernhard (2016), "Rotationally symmetric tilings with convex pentagons and hexagons", Elemente der Mathematik, 71 (4): 137–144, arXiv:1509.06297, doi:10.4171/em/310, ISSN 0013-6018, S2CID 119738738
Chavey 1989. Chavey, D. (1989), "Tilings by Regular Polygons—II: A Catalog of Tilings", Computers & Mathematics with Applications, 17 (1–3): 147–165, doi:10.1016/0898-1221(89)90156-9
Godrèche 1989. Godrèche, C. (1989), "The sphinx: a limit-periodic tiling of the plane", Journal of Physics A: Mathematical and General, 22 (24): L1163 – L1166, Bibcode:1989JPhA...22L1163G, doi:10.1088/0305-4470/22/24/006, MR 1030678
Gerver 2003. Gerver, M. L. (2003), "Theorems on tessellations by polygons", Sbornik: Mathematics, 194 (6): 879–895, Bibcode:2003SbMat.194..879G, doi:10.1070/sm2003v194n06abeh000743, S2CID 250813440
Frettlöh, Dirk; Garber, Alexey (2015), "Symmetries of monocoronal tilings", Discrete Mathematics & Theoretical Computer Science, 17 (2): 203–234, arXiv:1402.4658, doi:10.46298/dmtcs.2142, MR 3411398

ens-lyon.fr

perso.ens-lyon.fr

Rao 2017. Rao, Michaël (2017), Exhaustive search of convex pentagons which tile the plane (PDF), arXiv:1708.00274

github.com

"Mathematica code verifying Rao-convex-pentagon-tiling classification", GitHub

harvard.edu

ui.adsabs.harvard.edu

Godrèche 1989. Godrèche, C. (1989), "The sphinx: a limit-periodic tiling of the plane", Journal of Physics A: Mathematical and General, 22 (24): L1163 – L1166, Bibcode:1989JPhA...22L1163G, doi:10.1088/0305-4470/22/24/006, MR 1030678
Gerver 2003. Gerver, M. L. (2003), "Theorems on tessellations by polygons", Sbornik: Mathematics, 194 (6): 879–895, Bibcode:2003SbMat.194..879G, doi:10.1070/sm2003v194n06abeh000743, S2CID 250813440

jstor.org

Schattschneider 1978. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Schattschneider 1978, Fig 12. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766

maa.org

Schattschneider 1978. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Schattschneider 1978, Fig 12. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766

probabilitysports.com

Brian Galebach, "Welcome to my collection of n-uniform tilings!", probabilitysports.com

quantamagazine.org

Wolchover 2017. Wolchover, Natalie (11 July 2017), "Pentagon Tiling Proof Solves Century-Old Math Problem", Quanta Magazine
Marjorie Rice’s Secret Pentagons Quanta Magazine

semanticscholar.org

api.semanticscholar.org

Grünbaum & Shephard 1978. Grünbaum, Branko; Shephard, Geoffrey C. (1978), "Isohedral tilings of the plane by polygons", Commentarii Mathematici Helvetici, 53: 542–571, doi:10.1007/bf02566098, ISSN 0010-2571, S2CID 119897404
Mann, McLoud-Mann & Von Derau 2018. Mann, Casey; McLoud-Mann, Jennifer; Von Derau, David (2018), "Convex pentagons that admit $i$ -block transitive tilings", Geometriae Dedicata, 194 (1): 141–167, arXiv:1510.01186, doi:10.1007/s10711-017-0270-9, S2CID 119176351
Klaassen 2016. Klaassen, Bernhard (2016), "Rotationally symmetric tilings with convex pentagons and hexagons", Elemente der Mathematik, 71 (4): 137–144, arXiv:1509.06297, doi:10.4171/em/310, ISSN 0013-6018, S2CID 119738738
Gerver 2003. Gerver, M. L. (2003), "Theorems on tessellations by polygons", Sbornik: Mathematics, 194 (6): 879–895, Bibcode:2003SbMat.194..879G, doi:10.1070/sm2003v194n06abeh000743, S2CID 250813440

sites.google.com

Marjorie Rice, "Tessellations", Intriguing Tessellations, retrieved 22 August 2015 – via Google Sites

theguardian.com

Bellos 2015. Bellos, Alex (11 August 2015), "Attack on the pentagon results in discovery of new mathematical tile", The Guardian

uni-goettingen.de

gdz.sub.uni-goettingen.de

Reinhardt 1918, pp. 77–81 (caution: there is at least one obvious mistake within this paper, i.e. γ+δ angle sum needs to equal π, not 2π for the first two tiling types defined on page 77) Reinhardt, Karl (1918), Über die Zerlegung der Ebene in Polygone (Dissertation) (in German), Borna-Leipzig: Druck von Robert Noske

resolver.sub.uni-goettingen.de

Reinhardt 1918, pp. 77–81 (caution: there is at least one obvious mistake within this paper, i.e. γ+δ angle sum needs to equal π, not 2π for the first two tiling types defined on page 77) Reinhardt, Karl (1918), Über die Zerlegung der Ebene in Polygone (Dissertation) (in German), Borna-Leipzig: Druck von Robert Noske

wolframalpha.com

Cairo pentagonal tiling generated by a pentagon type 4 query and by a pentagon type 2 tiling query on wolframalpha.com (caution: the wolfram definition of pentagon type 2 tiling does not correspond with type 2 defined by Reinhardt in 1918)

worldcat.org

search.worldcat.org

Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Nirlee; Vieira, Luis Sordo; Wikner, Elena (2012-05-01), "Isoperimetric Pentagonal Tilings", Notices of the American Mathematical Society, 59 (5): 632, doi:10.1090/noti838, ISSN 0002-9920
Grünbaum & Shephard 1978. Grünbaum, Branko; Shephard, Geoffrey C. (1978), "Isohedral tilings of the plane by polygons", Commentarii Mathematici Helvetici, 53: 542–571, doi:10.1007/bf02566098, ISSN 0010-2571, S2CID 119897404
Schattschneider 1978. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Schattschneider 1978, Fig 12. Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.2307/2689644, ISSN 0025-570X, JSTOR 2689644, MR 0493766
Hirschhorn & Hunt 1985. Hirschhorn, M. D.; Hunt, D. C. (1985), "Equilateral convex pentagons which tile the plane" (PDF), Journal of Combinatorial Theory, Series A, 39 (1): 1–18, doi:10.1016/0097-3165(85)90078-0, ISSN 1096-0899, MR 0787713, retrieved 2020-10-30
Klaassen 2016. Klaassen, Bernhard (2016), "Rotationally symmetric tilings with convex pentagons and hexagons", Elemente der Mathematik, 71 (4): 137–144, arXiv:1509.06297, doi:10.4171/em/310, ISSN 0013-6018, S2CID 119738738