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Transactions of the American Mathematical Society

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The sets that are scissor congruent to an unbounded convex subset of the plane


Author: Sydell Perlmutter Gold
Journal: Trans. Amer. Math. Soc. 215 (1976), 99-117
MSC: Primary 52A05
DOI: https://doi.org/10.1090/S0002-9947-1976-0397544-9
MathSciNet review: 0397544
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Abstract: It is shown that an unbounded convex plane body is scissor congruent to the union of a congruent body with a finite number of arbitrary topological discs. It is proved that 'is scissor congruent to' is an equivalence relation. Thus two unbounded convex plane bodies are scissor congruent if and only if the union of one with a finite number of topological discs is scissor congruent to the other.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0397544-9
Keywords: Scissor congruent, unbounded figure, topological disc, topological half-plane, eventually convex, S-equivalent
Article copyright: © Copyright 1976 American Mathematical Society