Name
Title | ||
|---|---|---|
The optimality of a certain purely recursive dissection for a sequentially n-divisible square |
Abstract | ||
|---|---|---|
A dissection for a sequentially n-divisible square is a partition of a square into a number of polygons, not necessarily squares, which can be rearranged to form two squares, three squares, and so on, up to n squares successively. A dissection is called type-k iff k more pieces are needed to increase the maximum number n of composed squares by one. Ozawa found a general dissection of type-3, while Akiyama and Nakamura found a particular, "purely recursive" dissection of type-2. Nozaki has given a mixed procedure for a dissection of type-1.In this paper, we shall show that there is no type-1 purely recursive dissection for a sequentially n-divisible square. Therefore Akiyama and Nakamura's dissection is optimal with respect to the type, among the purely recursive dissections. The results have been published in previous papers [1,2,6,7]. In this paper, we give a detailed proof. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0925-7721(02)00047-0 | Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry |
Keywords | Field | DocType |
general dissection,purely recursive dissection,sequentially n-divisible square,sequentially n -divisible square,recursive dissection,detailed proof,maximum number n,type-k iff k,previous paper,mixed procedure | Discrete mathematics,Polygon,Combinatorics,Partition (number theory),Recursion,Mathematics | Journal |
Volume | Issue | ISSN |
24 | 1 | 0925-7721 |
Citations | PageRank | References |
5 | 0.75 | 2 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jin Akiyama | 1 | 8 | 3.05 |
| Gisaku Nakamura | 2 | 77 | 24.13 |
| Akihiro Nozaki | 3 | 38 | 11.00 |
| Ken'ichi Ozawa | 4 | 9 | 1.94 |
| Toshinori Sakai | 5 | 54 | 9.64 |