Abstract
Hi, Kyuta. You look bored.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Akiyama, Various Applications of Math (KonnaTokoronimo Suugaku ga) (in Japanese), Fusosya (2009)
O. Bagina, Tiling of the Plane with Convex Pentagons (in Russian), Vestnik KemGU, 4(48), (2011), 63-73
D. Beauquier and M. Nivat, On Translating One Polyomino To Tile the Plane, Discrete Comp. Geom. 6 (1991), 575-592
B. Atalay, Math and the Mona Lisa: The Art and Science of Leonard da Vinci, Harper Collins Publishers (2004)
COMAP eds, For All Practical Purposes: Introduction to Contemporary Mathematics 4th ed., W. H. Freeman (1997)
J. H. Conway, H. Burgiel and C. Goodman-Straus, The Symmetries of Things, A. K. Peters, Wellesley, MA (2008)
H. S. M. Coxeter, Introduction to Geometry (Second edition), John Wiley&Sons, Inc. (1980), First edition (1961)
H. S. M. Coxeter, Regular Polytopes, Courier, Dover (1973)
K. Enomoto, Infinite visions of Durer's octahedron in Melencolia I (in Japanese), Satani Gallery (1998)
E. S. Fedorov, Zapiski Mineralogicheskogo Impeatorskogo, S. Petersburgskog Obshchestva (2), 28 (1891)
H. Fukuda and G. Nakamura, From Escher to Crystal Structure (Escher no E kara Kessho Kouzou he) (in Japanese), Kaimeisya (2013), First edition (1983)
M. Gardner, On Tessellating the Plane with Convex Polygon Tiles. Scientific American, July, (1975), 112-117
M. Gardner, Penrose Tiles to Trapdoor Ciphers, W. H. Freeman and Company (1989).
B. Grünbaum, G. C. Shephard, Tilings And Patterns, W. H. Freeman and Company (1987)
P. M. Higgins, Mathematics for the Imagination, Oxford University Press (2002)
H. Nakamura, New Hokusai Kaleidoscope (Shin Hokusai Mangekyo) (in Japanese), Bijutu Syuppansha (2004)
C. A. Pickover, The Mαth βook, STERLING (2009)
G. Polya, P. Niggli, Zeitschrift für Kristallograhie und Mineralogie, 60, (1924), 278-298
K. Reinhardt, Über die Zerlegung der Ebene in Polygone, Dissertation, Universität Frankfurt (1918)
M. du Sautoy, Symmetry: A Journey into the Patterns of Nature, Harper Perennial (2009)
D. Schattschneider, Will It Tile? Try the Conway Criterion!, Mathematics Magazine Vol. 53 (Sept. 1980), No. 4. 224-233
D. Schattschneider, In Praise of Amateurs, in Mathematical Reactions (Klarner, D. A. ed.), 140-166 Dover, (1998), first printed in, Wadsworth (1981)
J. E. S. Socolar and J. M. Taylor, An aperiodic hexagonal tile, J. Comb. Theory 18(2011), 2207-2231
T. Sugimoto, T. Ogawa, Tiling Problem of Convex Pentagon, Forma, Vol. 15. No. 1 (2000), 75-79
T. Sugimoto, Convex Pentagons for Edge-to-Edge Tiling II, Graphs and Combinatorics, Vol. 31, No. 1 (2015), 281-298
D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, Penguin Books London (1991)
Wikipedia, Conway Criterion, http://en.wikipedia.org/wiki/Conway_criterion
The Gardian, Pentagonal-tiling, http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Japan
About this chapter
Cite this chapter
Akiyama, J., Matsunaga, K. (2015). Art From Tiling Patterns. In: Treks into Intuitive Geometry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55843-9_1
Download citation
DOI: https://doi.org/10.1007/978-4-431-55843-9_1
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55841-5
Online ISBN: 978-4-431-55843-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)