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 as follows: Hinge the parts of α like a string along the perimeter of α , then fix one of the parts to form β with the perimeter of α going into its interior and with its perimeter consisting of the dissection lines in the interior of α , without turning the surfaces over. In this paper we discuss a special case of Dudeney dissection where α is congruent to β , in particular, when all hinge points are on the vertices of the polygon α . We determine necessary and sufficient conditions under which such dissections exist.
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References
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Akiyama, J., Nakamura, G.: Congruent Dudeney dissections of polygons – Some hinge points on vertices, others interior to the sides of the polygon (to appear)
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Akiyama, J., Nakamura, G. (2003). Congruent Dudeney Dissections of Polygons. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_3
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DOI: https://doi.org/10.1007/978-3-540-44400-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
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