Partitioning a Regular n-gon into n+1 Convex Congruent Pieces is Impossible, for Sufficiently Large n
نویسندگان
چکیده
The interest in polygon decomposition emanates from the theoretical importance of the problem on one hand and the many applications that it has on the other. The decomposition problem has been extensively studied in the literature and yet variations of the problem remain open [3]. The existence of a huge literature on this problem can be informally explained by the fact that there are numerous ways in which we can decompose a polygon and there are many types of polygons to decompose. Decomposition can be defined as partitioning a polygon into components according to a set of rules. In other words, each kind of decomposition has a set of constraints either on the type of the pieces, the number of pieces, the length of the cuts, the areas of the partitions. In this paper, we discuss the following problem posed by Joseph O’Rourke at the Fall Workshop on Computational Geometry in 2004: Is it possible to partition a regular n-gon into n+1 congruent pieces? It is obviously possible for the equilateral triangle and the square as shown below. However, is it ever possible for n ≥ 5?
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