An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube? | Zendy

Kreinovich Vladik | Zendy; Kosheleva Olga | Zendy

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An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube?

Author(s) -

Kreinovich Vladik,

Kosheleva Olga

Publication year - 1994

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19940400105

Subject(s) - uncountable set , mathematics , cube (algebra) , tetrahedron , decidability , combinatorics , discrete mathematics , geometry , countable set

It is known (see Rapp [9]) that elementary geometry with the additional quantifier “there exist uncountably many” is decidable. We show that this decidability helps in solving the following problem from combinatorial geometry: does there exist an uncountable family of pairwise non‐congruent tetrahedra that are n ‐equidecomposable with a cube? Mathematics Subject Classification: 03B25, 03C80, 51M04, 52B05, 52B10.

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