HILBERT'S 23 PROBLEMS
Paris, 1900
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SOLVEDPARTIALLY SOLVEDOPENTOO VAGUE
#3
SOLVED
Equidecomposability of Polyhedra
Max Dehn (1900) (1900)
Can two polyhedra of equal volume always be cut into finitely many pieces and reassembled into each other?
HISTORY
Dehn solved this almost immediately after Hilbert posed it, showing two tetrahedra of equal volume may not be equidecomposable. The Dehn invariant provides the obstruction.
The first of Hilbert's problems to be solved. Introduced the Dehn invariant, now fundamental in geometric topology.
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