Perspectives on scissors congruence

Zakharevich, Inna

doi:10.1090/bull/1527

Perspectives on scissors congruence

Author: Inna Zakharevich
Journal: Bull. Amer. Math. Soc. 53 (2016), 269-294
MSC (2010): Primary 52B45
DOI: https://doi.org/10.1090/bull/1527
Published electronically: January 25, 2016
MathSciNet review: 3474308
Full-text PDF Free Access

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Abstract: In this paper we give a short introduction to the different theories of scissors congruence. We begin with classical scissors congruence, which considers equivalence classes of polyhedra under dissection. We then move to multi-dimensional scissors congruence along the lines of McMullen's polytope algebra and then to the Grothendieck ring of varieties. Tying our discussion together is the question of whether algebraic invariants are sufficient to distinguish scissors congruence classes.

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