Sequentially Divisible Dissections of Simple Polygons

A k-dissection D of a polygon P, is a partition of P into a set of subpolygons {Q1, . . . , Qm} with disjoint interiors such that these can be reassembled to form k polygons P1, . . . , Pk all similar to P. D is called non-trivial if none of {Q1, . . . , Qm} is similar to P. In this paper we show that any convex n-gon has a k-dissection (resp. sequential dissection) with (k - 1)n + 1 pieces, n 5. Let k 2 and n 3 be integers and let P be an n-gon. We show that if P is a convex polygon and n 5, then there exists a dissection of P consisting of at most (m-1)n+1 polygons which combine to form sequentially 2, 3,

• Type: Conference
• Year: 2000
• Where: JCDCG
• Authors: Jin Akiyama, Toshinori Sakai, Jorge Urrutia
• Keywords: Convex Polygon, Discrete Geometry, JCDCG 2000, Polygon P, Polygons