Making Patterns on the Surfaces of Swing-Hinged Dissections

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Reference

Reza Sarhangi: Making Patterns on the Surfaces of Swing-Hinged Dissections. In: Bridges 2008. Pages 251–258

DOI

Abstract

The article presents some examples regarding the illustrations of patterns and designs on the surfaces of some swing- hinged dissections. These patterns are made in a way that when they are swung from one shape of the dissection to another, the patterns are also changed along with the shapes.

Extended Abstract

Bibtex

Used References

[1] Allman, George Johnston. Greek Geometry from Thales to Euclid. Hodges, Figgis&Co., Dublin, 1889.

[2] Anonymous. Interlocks of Similar or Complementary Figures. Paris: Biblioth`eque Nationale, ancien fonds. Persan 169, ff. 180r–199v.

[3] Buzjani Abûl-Wefâ. On the Geometric Constructions Necessary for the Artisan. There are four known hand-written copies of this treatise. One is in Arabic and the other three are in Persian. The original work was written in Arabic, the scientific language of the 10th century, but it is no longer exists. Each of the surviving copies has some missing information and chapters. The surviving Arabic, although not original, is more complete than the other three surviving copies. The Arabic edition is kept in the library of Ayasofya, Istanbul, Turkey. The most famous of the other three in Persian is the copy which is kept in the National Library in Paris, France. This copy includes the Interlocks amendment.

[4] Dudeney, Henry E. The Canterbury Puzzles and Other Curious Problems. W. Heinemann, London, 1907.

[5] Dudeney, Henry E. Perplexities. Monthly puzzle column in The Strand Magazine from May, 1910 through June, 1930.

[6] Dudeney, Henry E. Puzzles and Prizes. Column in the Weekly Dispatch, April 19, 1896–March 27, 1904.

[7] Frederickson, Greg N. Dissections Plane & Fancy. Cambridge University Press, New York, 1997.

[8] Frederickson, Greg N. Hinged Dissections: Swinging and Twisting. Cambridge University Press, New York, 2002.

[9] Frederickson, Greg N. the manifold beauty of piano-Hinged Dissections, Renaissance Banff Canada, Bridges Conference Proceedings, PP. 1-8, 2005.

[10] Frederickson, Greg N. Symmetry and Structure in Twist-Hinged Dissections of Polygonal Rings and Polygonal Anti-Rings, Bridges Donostia, Spain, Conference Proceedings, PP. 21-28, 2007.

[11] Jablan, Slavik. Modularity in Science and Art, Visual Mathematics Journal, Vol. 4, Number 1, 2002.

[12] Jazbi, S. A. (translator and editor), ‫ آاربرد هند سه درعمل‬:‫ هند سه ايرانى‬, Applied Geometry, Soroush Press, ISBN 964 435 201 7, Tehran 1997.

[13] Lindgren, Harry. Geometric Dissections. Australian Mathematics Teacher, 7, 1951.

[14] Loyd, Sam. Weekly puzzle column in Tit-Bits, starting in Oct. 3, 1896 and continuing into 1897.

[15] Loyd, Sam. Mental Gymnastics. Puzzle column in Sunday edition of Philadelphia Inquirer, October 23, 1898–1901.

[16] Mott-Smith, Geoffrey, Mathematical Puzzles for Beginners and Enthusiasts, Philadelphia, Blakiston, 1946, reprinted by Dover Publications, New York, 1954.

[17] Özdural, Alpay. Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World. Historia Mathematica, 27:171–201, 2000.

[18] Perigal, Henry. On Geometric Dissections and Transformations, Messenger of Mathematics 2, 103-5

[19] Sarhangi, Reza and Slavik Jablan, Elementary Constructions of Persian Mosaics, Math Horizons, MAA Publuication, September 2006.

[20] Theobald, Gavin. Geometric Dissections. http://home.btconnect.com/GavinTheobald/HTML/Index.html.

[21] The Journal of the Maze and Labyrinth Research Group http://www.labyrinthos.net/.


Links

Full Text

http://archive.bridgesmathart.org/2008/bridges2008-251.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2008/bridges2008-251.html