Efficient Regular Polygon Dissections

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). Key Words and Phrases: Dissections, Glass-cuts, Polygonal cuts, Regular polygons, Squares.

• Type: Conference
• Year: 1998
• Where: JCDCG
• Authors: Evangelos Kranakis, Danny Krizanc, Jorge Urrutia
• Keywords: Discrete Geometry, JCDCG 1998, Minimum Number, Polygonal Cuts, Regular