Geometric Factors and the Well Dressed Solids of Archimedes

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Stan Spencer: Geometric Factors and the Well Dressed Solids of Archimedes. In: Bridges 2017, Pages 167–174.

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Abstract

I have shown, in previous papers, that any regular polygon with n sides can be dissected into a set of isosceles triangles. These same triangles can be used to create other regular polygons with m sides provided that m is a factor of n. An enlarged version of each triangle can be created using the same isosceles triangles. In this paper I have shown how these ideas can be used to create Archimedean solids from the dissection of a single polygon. Well Dressing is a tradition in many small villages in the Pennine areas of rural England in which village wells are decorated with mosaics made from natural materials. The polygons for these solids can be in the form of an irregular tiling or a fractal. In the case of a fractal pattern I have used decorations from the Well Dressing at Hodthorpe Primary School as an inspiration for for colour choices and a source of images for decorating Archimedian solids

Extended Abstract

Bibtex

@inproceedings{bridges2017:167,
 author      = {Stan Spencer},
 title       = {Geometric Factors and the Well Dressed Solids of Archimedes},
 pages       = {167--174},
 booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
 year        = {2017},
 editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
 isbn        = {978-1-938664-22-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-167.pdf}}
}

Used References

[1] Stanley Spencer. An Introduction to the Tiling Properties of Precious Triangles, In Javier Barrallo, Nathaniel Friedman, Juan Antonio Maldonado, Jose Martinez-Aroza, Reza Sarhangi and Carlo Sequin, editors, Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003,pages 291–298, ISBN 1099-6702. University of Granada, Granada, Spain. Available online at url http://archive.bridgesmathart.org/2003/bridges2003-291.html (as of April 20 2017)

[2] Stanley Spencer. Creating Self Similar Tiling Patterns and Fractals using the Geometric Factors of a Regular Polygon, In Gary Greenfield, George Hart and Reza Sarhangi, editors, Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pages 279–284, ISBN 978-1-938664-11-3. Tessellations Publishing, Phoenix, Arizon. Available online at url http://archive.bridgesmathart.org/2014/bridges2014-279.html (as of April 20 2017)

[3] James Mai. Juan Gris’ Color Symmetries, In Gary Greenfield, George Hart and Reza Sarhangi, editors, Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pages 197– 204, ISBN 978-1-938664-11-3. Tessellations Publishing, Phoenix, Arizon. Available online at url http://archive.bridgesmathart.org/2014/bridges2014-197.html (as of April 20 2017)

[4] Glyn Williams. Welldressing Venues. Available online at url http://welldressing.com/venue.php (as of April 20 2017)

[5] Glyn Williams. Welldressing pictures. Available online at url http://welldressing.com/photo.php (as of April 20 2017)

[6] Rod Kirkpatrick video. Available online at url https://www.youtube.com/watch?v=jSvIf7OSmTU (as of April 20 2017)


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