The Convex Configurations of Dissection Puzzles with Seven Pieces

• Kazuho Katsumata

  School of Information Science, Japan Advanced Institute of Science and Technology

• Ryuhei Uehara

  School of Information Science, Japan Advanced Institute of Science and Technology

抄録

The most famous dissection puzzle is the tangram, which originated in China more than two centuries ago. From around the same time, there is a similar Japanese puzzle called Sei Shonagon Chie no Ita. Both are derived by cutting a square of material with straight incisions into seven different-sized pieces, and each piece consists of a few identical right isosceles triangle units. The right isosceles triangle unit is of 1/16 of the square, and the set of 16 units can form 20 different convex polygons. It is known that the tangram can form thirteen convex polygons among 20 convex polygons, and the Sei Shonagon Chie no Ita can form sixteen among them. Therefore, in a sense, the Sei Shonagon Chie no Ita is more expressive than the tangram. Last year, Fox-Epstein and Uehara proposed a more expressive pattern that can form nineteen convex polygons, and show that no set of seven pieces made from sixteen identical right isosceles triangles can form 20. In this paper, we refine their analysis, obtain four expressive patterns that satisfy the condition, and show that these four patterns are all.

収録刊行物

• 情報処理学会研究報告. AL, アルゴリズム研究会報告

  情報処理学会研究報告. AL, アルゴリズム研究会報告 2015 (9), 1-4, 2015-02-24

  一般社団法人情報処理学会

詳細情報

• CRID: 1571980077801445632
• NII論文ID: 110009877675
• NII書誌ID: AN1009593X
• ISSN: 09196072
• 本文言語コード: en
• データソース種別:
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