IEICE TRANSACTIONS on Fundamentals
The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.6 pp.1084-1089
- Publication Date
- 2016/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.1084
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Eli FOX-EPSTEIN
Brown University
Kazuho KATSUMATA
JAIST
Ryuhei UEHARA
JAIST
Keyword
Latest Issue
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Eli FOX-EPSTEIN, Kazuho KATSUMATA, Ryuhei UEHARA, "The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 6, pp. 1084-1089, June 2016, 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1084/_p
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@ARTICLE{e99-a_6_1084,
author={Eli FOX-EPSTEIN, Kazuho KATSUMATA, Ryuhei UEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces},
year={2016},
volume={E99-A},
number={6},
pages={1084-1089},
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.},
keywords={},
doi={10.1587/transfun.E99.A.1084},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1084
EP - 1089
AU - Eli FOX-EPSTEIN
AU - Kazuho KATSUMATA
AU - Ryuhei UEHARA
PY - 2016
DO - 10.1587/transfun.E99.A.1084
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2016
AB - 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.
ER -
English
