Efficient Regular Polygon Dissections |
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Authors: | Evangelos Kranakis Danny Krizanc Jorge Urrutia |
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Institution: | (1) School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada;(2) School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada;(3) School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, K1N 9B4, Canada |
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Abstract: | We study the minimum number g(m,n) (respectively, p(m,n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that n/2 -2 g(4,n) (n/2) + o(n) and n/4 g(n,4) (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4,n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that n/4 p(4,n) (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m,n) and p(m,n). |
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Keywords: | dissections glass-cuts polygonal cuts regular polygons squares |
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