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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13708

Title: Convex Configurations on Nana-kin-san Puzzle
Authors: Horiyama, Takashi
Uehara, Ryuhei
Hosoya, Haruo
Keywords: silhouette puzzle
nana-kin-san puzzle
enumeration algorithm
convex polygon
Issue Date: 2016-06
Publisher: Schloss Dagstuhl
Magazine name: LIPIcs (8th International Conference on Fun with Algorithms)
Volume: 49
Number: FUN 2016
Start page: 20:1
End page: 20:14
DOI: 10.4230/LIPIcs.FUN.2016.20
Abstract: We investigate a silhouette puzzle that is recently developed based on the golden ratio. Traditional silhouette puzzles are based on a simple tile. For example, the tangram is based on isosceles right triangles; that is, each of seven pieces is formed by gluing some identical isosceles right triangles. Using the property, we can analyze it by hand, that is, without computer. On the other hand, if each piece has no special property, it is quite hard even using computer since we have to handle real numbers without numerical errors during computation. The new silhouette puzzle is between them; each of seven pieces is not based on integer length and right angles, but basedon golden ratio, which admits us to represent these seven pieces in some nontrivial way. Based on the property, we develop an algorithm to handle the puzzle, and our algorithm succeeded to enumerate all convex shapes that can be made by the puzzle pieces. It is known that the tangram and another classic silhouette puzzle known as Sei-shonagon chie no ita can form 13 and 16 convex shapes, respectively. The new puzzle, Nana-kin-san puzzle, admits to form 62 different convex shapes.
Rights: ⓒTakashi Horiyama, Ryuhei Uehara, and Haruo Hosoya; licensed under Creative Commons License CC-BY. 8th International Conference on Fun with Algorithms. Editor: Erik D. Demaine and Fabrizio Grandoni ; pp. 20:1–20:14.
URI: http://hdl.handle.net/10119/13708
Material Type: publisher
Appears in Collections:b11-1. 会議発表論文・発表資料 (Conference Papers)

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