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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13778

Title: The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces
Authors: Fox-Epstein, Eli
Katsumata, Kazuho
Uehara, Ryuhei
Keywords: dissection puzzle
Sei Shonagon Chie no Ita
silhouette puzzle
Issue Date: 2016-06
Publisher: 電子情報通信学会
Magazine name: IEICE transactions on fundamentals of electronics, communications and computer sciences
Volume: E99-A
Number: 6
Start page: 1084
End page: 1089
DOI: 10.1587/transfun.E99.A.1084
Abstract: The most famous silhouette 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 pieces of varying shapes, and each can be decomposed into sixteen non-overlapping identical right isosceles triangles. It is known that the pieces of the tangram can form thirteen distinct convex polygons. We first show that the Sei Shonagon Chie no Ita can form sixteen. Therefore, in a sense, the Sei Shonagon Chie no Ita is more expressive than the tangram. We also propose more expressive patterns built from the same 16 identical right isosceles triangles that can form nineteen convex polygons. There exist exactly four sets of seven pieces that can form nineteen convex polygons. We show no set of seven pieces can form at least 20 convex polygons, and demonstrate that eleven pieces made from sixteen identical isosceles right triangles are necessary and sufficient to form 20 convex polygons. Moreover, no set of six pieces can form nineteen convex polygons.
Rights: Copyright (C)2016 IEICE. Eli Fox-Epstein, Kazuho Katsumata, and Ryuhei Uehara, IEICE transactions on fundamentals of electronics, communications and computer sciences, E99-A(6), 2016, 1084-1089. http://www.ieice.org/jpn/trans_online/
URI: http://hdl.handle.net/10119/13778
Material Type: publisher
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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