Further Information
In light of Dehn's theorem above, one might ask "which polyhedra are scissors-congruent"? Sydler (1965) showed that two polyhedra are scissors-congruent if and only if they have the same volume and the same Dehn invariant. Børge Jessen later extended Sydler's results to four dimensions. In 1990, Dupont and Sah provided a simpler proof of Sydler's result by reinterpreting it as a theorem about the homology of certain classical groups.
Debrunner showed in 1980 that the Dehn invariant of any polyhedron with which all of three-dimensional space can be tiled periodically is zero.
Read more about this topic: Hilbert's Third Problem
Famous quotes containing the word information:
“Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it.”
—Samuel Johnson (17091784)
“On the breasts of a barmaid in Sale
Were tattooed the prices of ale;
And on her behind
For the sake of the blind
Was the same information in Braille.”
—Anonymous.