Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--

Jin AKIYAMA; Gisaku NAKAMURA

Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--

Jin AKIYAMA, Gisaku NAKAMURA

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Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β in the following way. Hinge the parts of α like a chain along the perimeter of α, then fix one of the parts and without turning the pieces over, rotate the remaining parts about the fixed part to form β in such a way that the entire perimeter of α is in the interior of β and the perimeter of β consists of the dissection lines formerly in the interior of α . In this paper we discuss a special type of Dudeney dissection of convex polygons in which α is congruent to β and call it a congruent Dudeney dissection. In particular, we consider the case where all hinge points are interior to the sides of the polygon α. A convex polygon which has a congruent Dudeney dissection is called a chameleon. We determine all convex polygons which are chameleons.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.5 pp.978-986

Publication Date: 2003/05/01

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Type of Manuscript: Special Section INVITED PAPER (Special Section on Discrete Mathematics and Its Applications)

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Jin AKIYAMA, Gisaku NAKAMURA, "Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 5, pp. 978-986, May 2003, doi: .
Abstract: Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β in the following way. Hinge the parts of α like a chain along the perimeter of α, then fix one of the parts and without turning the pieces over, rotate the remaining parts about the fixed part to form β in such a way that the entire perimeter of α is in the interior of β and the perimeter of β consists of the dissection lines formerly in the interior of α . In this paper we discuss a special type of Dudeney dissection of convex polygons in which α is congruent to β and call it a congruent Dudeney dissection. In particular, we consider the case where all hinge points are interior to the sides of the polygon α. A convex polygon which has a congruent Dudeney dissection is called a chameleon. We determine all convex polygons which are chameleons.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_5_978/_p

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@ARTICLE{e86-a_5_978,
author={Jin AKIYAMA, Gisaku NAKAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--},
year={2003},
volume={E86-A},
number={5},
pages={978-986},
abstract={Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β in the following way. Hinge the parts of α like a chain along the perimeter of α, then fix one of the parts and without turning the pieces over, rotate the remaining parts about the fixed part to form β in such a way that the entire perimeter of α is in the interior of β and the perimeter of β consists of the dissection lines formerly in the interior of α . In this paper we discuss a special type of Dudeney dissection of convex polygons in which α is congruent to β and call it a congruent Dudeney dissection. In particular, we consider the case where all hinge points are interior to the sides of the polygon α. A convex polygon which has a congruent Dudeney dissection is called a chameleon. We determine all convex polygons which are chameleons.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 978
EP - 986
AU - Jin AKIYAMA
AU - Gisaku NAKAMURA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2003
AB - Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β in the following way. Hinge the parts of α like a chain along the perimeter of α, then fix one of the parts and without turning the pieces over, rotate the remaining parts about the fixed part to form β in such a way that the entire perimeter of α is in the interior of β and the perimeter of β consists of the dissection lines formerly in the interior of α . In this paper we discuss a special type of Dudeney dissection of convex polygons in which α is congruent to β and call it a congruent Dudeney dissection. In particular, we consider the case where all hinge points are interior to the sides of the polygon α. A convex polygon which has a congruent Dudeney dissection is called a chameleon. We determine all convex polygons which are chameleons.
ER -