most citedConvex fair partitions into an arbitrary number of pieces

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math.MG2026★ 7 cited

Convex fair partitions into an arbitrary number of pieces

Arseniy Akopyan, Sergey Avvakumov, Roman Karasev

We prove that any convex body in the plane can be partitioned into convex parts of equal areas and perimeters for any integer ; this result was previously known for pri…

math.MG2026

Rogers's proof of Vaaler's theorem

Roman Karasev

We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.