Mathematics · the experiment
Cut in four dimensions
A question asked in 1933, a dimension where nobody knows the answer, seven balls and 23,494 boxes. Four questions, from beginner to expert, on the new bound for the Borsuk number.
1 · The result2 · The old bound3 · The machine4 · The gap
1 · Say what is proved
Beginner
What did the four mathematicians prove in four dimensions?
2 · Work out Lassak's bound
Lassak's general bound says b_n ≤ 2ⁿ⁻¹ + 1, where n is the dimension.
Intermediate
What does this bound give in four dimensions?
3 · Explain why it is a proof
Expert
Why does the computer calculation count as a proof, not just a simulation?
4 · Place the Borsuk number
Expert
After this article, what do we know about the Borsuk number b₄?
Shape cut
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