Folding Pseudo-Stars that are Cyclicly Hinged
Inhaltsverzeichnis
Reference
Greg N. Frederickson: Folding Pseudo-Stars that are Cyclicly Hinged. In: Bridges 2015. Pages 1–8
DOI
Abstract
Motivated by a (layered) folding dissection of a 2-high {10/3}-star to a 4-high {5/2}-star, we identify an infinite class of folding dissections for pseudo-stars for which the dissections are cyclicly hinged. In addition to folding dissections of 2-high to 4-high pseudo-stars, the class includes folding dissections of 2-high to (2h)-high pseudo-stars for any whole number h, as well as folding dissections of (2h)-high to (2h′)-high pseudo-stars where h and h′ are whole numbers such that gcd(h, h′) = 1. The total number of pieces in each of these folding dissections is the sum of the number of points in both stars.
Extended Abstract
Bibtex
@inproceedings{bridges2015:1,
author = {Greg N. Frederickson},
title = {Folding Pseudo-Stars that are Cyclicly Hinged },
pages = {1--8},
booktitle = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
year = {2015},
editor = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
isbn = {978-1-938664-15-1},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-1.html }}
}
Used References
[1] C. S. Elliott. An extension to polygram shapes and some new dissections. Journal of Recreational Mathematics, 27(4):277–284, 1995.
[2] Greg N. Frederickson. Dissections Plane & Fancy. Cambridge University Press, New York, 1997.
[3] Greg N. Frederickson. Hinged Dissections: Swinging and Twisting. Cambridge University Press, New York, 2002.
[4] Greg N. Frederickson. Piano-Hinged Dissections: Time to Fold! A K Peters, Wellesley, MA, 2006.
[5] Greg N. Frederickson. Dissecting and folding stacked geometric figures. Powerpoint presentation at the DIMACS Workshop on Algorithmic Mathematical Art: Special Cases and Their Applications, Rutgers University, Piscataway, NJ., 2009.
[6] Greg N. Frederickson. My parade of algorithmic mathematical art. In Robert Bosch, DouglasMcKenna, and Reza Sarhangi, editors, Bridges Towson: Mathematics, Music, Art, Architecture, Culture, Proceedings 2012, pages 41–48, Towson, MD, 2012. Tessellations Publishing.
[7] Harry Lindgren. Geometric Dissections. D. Van Nostrand Company, Princeton, New Jersey, 1964.
Links
Full Text
http://archive.bridgesmathart.org/2015/bridges2015-1.pdf
