An elementary proof of borsuk theorem
arXiv:1010.1990
Abstract
In 1933, Borsuk conjectured that any bounded d-dimensional set of nonzero diameter can be broken into d + 1 parts of smaller diameter. This conjecture was disproved for large enough d, though it is true for low dimensional cases. The paper provides an alternative proof for d = 2 case.
2 pages, 1 figure, this note is one of the results of my participation in `Math in Moscow' program