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A Note on the Purely Recursive Dissection for a Sequentially
n
-Divisible Square
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A Note on the Purely Recursive Dissection for a Sequentially n-Divisible Square
Jin Akiyama7  , Gisaku Nakamura7, Akihiro Nozaki8 and Ken’ichi Ozawa9
| (7) |
Research Institute of Educational Development, Tokai University, 2-84-2 Tomiyaga, Shibuya-ku, Tokyo 151-0063, Japan |
| (8) |
School of Social Information Studies, Otsuma Women’s University, 2-7-1 Karakida, Tama-shi, Tokyo 206-8540, Japan |
| (9) |
Hihashino Highschool, 112-1 Nihongi, Iruma-shi, Saitama 358-8558, Japan |
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 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 note, 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.
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