Premium
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.