Pythagorean tiling (English Wikipedia)

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

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Martini, Horst; Makai, Endre; Soltan, Valeriu (1998), "Unilateral tilings of the plane with squares of three sizes", Beiträge zur Algebra und Geometrie, 39 (2): 481–495, MR 1642720.
Aguiló, Francesc; Fiol, Miquel Angel; Fiol, Maria Lluïsa (2000), "Periodic tilings as a dissection method", American Mathematical Monthly, 107 (4): 341–352, doi:10.2307/2589179, JSTOR 2589179, MR 1763064.
The truth of his conjecture for two-dimensional tilings was known already to Keller, but it was since proven false for dimensions eight and above. For a recent survey on results related to this conjecture, see Zong, Chuanming (2005), "What is known about unit cubes", Bulletin of the American Mathematical Society, New Series, 42 (2): 181–211, doi:10.1090/S0273-0979-05-01050-5, MR 2133310.
Bölcskei, Attila (2001), "Filling space with cubes of two sizes", Publicationes Mathematicae Debrecen, 59 (3–4): 317–326, doi:10.5486/PMD.2001.2480, MR 1874434, S2CID 226270246. See also Dawson (1984), which includes an illustration of the three-dimensional tiling, credited to "Rogers" but cited to a 1960 paper by Richard K. Guy: Dawson, R. J. M. (1984), "On filling space with different integer cubes", Journal of Combinatorial Theory, Series A, 36 (2): 221–229, doi:10.1016/0097-3165(84)90007-4, MR 0734979.
Figure 3 of Danzer, Ludwig; Grünbaum, Branko; Shephard, G. C. (1982), "Unsolved Problems: Can All Tiles of a Tiling Have Five-Fold Symmetry?", The American Mathematical Monthly, 89 (8): 568–570+583–585, doi:10.2307/2320829, JSTOR 2320829, MR 1540019.

archive.org

Wells, David (1991), "two squares tessellation", The Penguin Dictionary of Curious and Interesting Geometry, New York: Penguin Books, pp. 260–261, ISBN 0-14-011813-6.

books.google.com

Editors of Fine Homebuilding (2013), Bathroom Remodeling, Taunton Press, p. 45, ISBN 978-1-62710-078-6. A schematic diagram illustrating this floor tile pattern appears earlier, on p. 42.
Ostermann, Alexander; Wanner, Gerhard (2012), "Thales and Pythagoras", Geometry by Its History, Undergraduate Texts in Mathematics, Springer, pp. 3–26, doi:10.1007/978-3-642-29163-0_1. See in particular pp. 15–16.

doi.org

Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs" (PDF), Math Horizons, 11 (2): 5–8, doi:10.1080/10724117.2003.12021741, S2CID 126000048. Reprinted in Haunsperger, Deanna; Kennedy, Stephen (2007), The Edge of the Universe: Celebrating Ten Years of Math Horizons, Spectrum Series, Mathematical Association of America, pp. 295–298, ISBN 978-0-88385-555-3. See also Alsina, Claudi; Nelsen, Roger B. (2010), Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions, vol. 42, Mathematical Association of America, pp. 168–169, ISBN 978-0-88385-348-1.
Radin, C. (1994), "The Pinwheel Tilings of the Plane", Annals of Mathematics, 139 (3): 661–702, doi:10.2307/2118575, JSTOR 2118575
Aguiló, Francesc; Fiol, Miquel Angel; Fiol, Maria Lluïsa (2000), "Periodic tilings as a dissection method", American Mathematical Monthly, 107 (4): 341–352, doi:10.2307/2589179, JSTOR 2589179, MR 1763064.
Ostermann, Alexander; Wanner, Gerhard (2012), "Thales and Pythagoras", Geometry by Its History, Undergraduate Texts in Mathematics, Springer, pp. 3–26, doi:10.1007/978-3-642-29163-0_1. See in particular pp. 15–16.
Steurer, Walter; Deloudi, Sofia (2009), "3.5.3.7 The Klotz construction", Crystallography of Quasicrystals: Concepts, Methods and Structures, Springer Series in Materials Science, vol. 126, Springer, pp. 91–92, doi:10.1007/978-3-642-01899-2, ISBN 978-3-642-01898-5.
Sánchez, José; Escrig, Félix (December 2011), "Frames designed by Leonardo with short pieces: An analytical approach", International Journal of Space Structures, 26 (4): 289–302, doi:10.1260/0266-3511.26.4.289, S2CID 108639647.
The truth of his conjecture for two-dimensional tilings was known already to Keller, but it was since proven false for dimensions eight and above. For a recent survey on results related to this conjecture, see Zong, Chuanming (2005), "What is known about unit cubes", Bulletin of the American Mathematical Society, New Series, 42 (2): 181–211, doi:10.1090/S0273-0979-05-01050-5, MR 2133310.
Bölcskei, Attila (2001), "Filling space with cubes of two sizes", Publicationes Mathematicae Debrecen, 59 (3–4): 317–326, doi:10.5486/PMD.2001.2480, MR 1874434, S2CID 226270246. See also Dawson (1984), which includes an illustration of the three-dimensional tiling, credited to "Rogers" but cited to a 1960 paper by Richard K. Guy: Dawson, R. J. M. (1984), "On filling space with different integer cubes", Journal of Combinatorial Theory, Series A, 36 (2): 221–229, doi:10.1016/0097-3165(84)90007-4, MR 0734979.
Burns, Aidan (1994), "78.13 Fractal tilings", Mathematical Gazette, 78 (482): 193–196, doi:10.2307/3618577, JSTOR 3618577, S2CID 126185324. Rigby, John (1995), "79.51 Tiling the plane with similar polygons of two sizes", Mathematical Gazette, 79 (486): 560–561, doi:10.2307/3618091, JSTOR 3618091, S2CID 125458495.
Figure 3 of Danzer, Ludwig; Grünbaum, Branko; Shephard, G. C. (1982), "Unsolved Problems: Can All Tiles of a Tiling Have Five-Fold Symmetry?", The American Mathematical Monthly, 89 (8): 568–570+583–585, doi:10.2307/2320829, JSTOR 2320829, MR 1540019.

emis.de

Martini, Horst; Makai, Endre; Soltan, Valeriu (1998), "Unilateral tilings of the plane with squares of three sizes", Beiträge zur Algebra und Geometrie, 39 (2): 481–495, MR 1642720.

jstor.org

Radin, C. (1994), "The Pinwheel Tilings of the Plane", Annals of Mathematics, 139 (3): 661–702, doi:10.2307/2118575, JSTOR 2118575
Aguiló, Francesc; Fiol, Miquel Angel; Fiol, Maria Lluïsa (2000), "Periodic tilings as a dissection method", American Mathematical Monthly, 107 (4): 341–352, doi:10.2307/2589179, JSTOR 2589179, MR 1763064.
Burns, Aidan (1994), "78.13 Fractal tilings", Mathematical Gazette, 78 (482): 193–196, doi:10.2307/3618577, JSTOR 3618577, S2CID 126185324. Rigby, John (1995), "79.51 Tiling the plane with similar polygons of two sizes", Mathematical Gazette, 79 (486): 560–561, doi:10.2307/3618091, JSTOR 3618091, S2CID 125458495.
Figure 3 of Danzer, Ludwig; Grünbaum, Branko; Shephard, G. C. (1982), "Unsolved Problems: Can All Tiles of a Tiling Have Five-Fold Symmetry?", The American Mathematical Monthly, 89 (8): 568–570+583–585, doi:10.2307/2320829, JSTOR 2320829, MR 1540019.

semanticscholar.org

api.semanticscholar.org

Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs" (PDF), Math Horizons, 11 (2): 5–8, doi:10.1080/10724117.2003.12021741, S2CID 126000048. Reprinted in Haunsperger, Deanna; Kennedy, Stephen (2007), The Edge of the Universe: Celebrating Ten Years of Math Horizons, Spectrum Series, Mathematical Association of America, pp. 295–298, ISBN 978-0-88385-555-3. See also Alsina, Claudi; Nelsen, Roger B. (2010), Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions, vol. 42, Mathematical Association of America, pp. 168–169, ISBN 978-0-88385-348-1.
Sánchez, José; Escrig, Félix (December 2011), "Frames designed by Leonardo with short pieces: An analytical approach", International Journal of Space Structures, 26 (4): 289–302, doi:10.1260/0266-3511.26.4.289, S2CID 108639647.
Bölcskei, Attila (2001), "Filling space with cubes of two sizes", Publicationes Mathematicae Debrecen, 59 (3–4): 317–326, doi:10.5486/PMD.2001.2480, MR 1874434, S2CID 226270246. See also Dawson (1984), which includes an illustration of the three-dimensional tiling, credited to "Rogers" but cited to a 1960 paper by Richard K. Guy: Dawson, R. J. M. (1984), "On filling space with different integer cubes", Journal of Combinatorial Theory, Series A, 36 (2): 221–229, doi:10.1016/0097-3165(84)90007-4, MR 0734979.
Burns, Aidan (1994), "78.13 Fractal tilings", Mathematical Gazette, 78 (482): 193–196, doi:10.2307/3618577, JSTOR 3618577, S2CID 126185324. Rigby, John (1995), "79.51 Tiling the plane with similar polygons of two sizes", Mathematical Gazette, 79 (486): 560–561, doi:10.2307/3618091, JSTOR 3618091, S2CID 125458495.

sfgate.com

homeguides.sfgate.com

"How to Install Hopscotch Pattern Tiles", Home Guides, San Francisco Chronicle, retrieved 2016-12-12.

upenn.edu

www-stat.wharton.upenn.edu

Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs" (PDF), Math Horizons, 11 (2): 5–8, doi:10.1080/10724117.2003.12021741, S2CID 126000048. Reprinted in Haunsperger, Deanna; Kennedy, Stephen (2007), The Edge of the Universe: Celebrating Ten Years of Math Horizons, Spectrum Series, Mathematical Association of America, pp. 295–298, ISBN 978-0-88385-555-3. See also Alsina, Claudi; Nelsen, Roger B. (2010), Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions, vol. 42, Mathematical Association of America, pp. 168–169, ISBN 978-0-88385-348-1.