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math.MG2026
Mutually touching cylinders: Littlewood's seven, and at most ten in general
Ivan Matić, Kenta Kitamura, Radoš Radoičić +1
We give a computer-assisted proof that at most seven congruent infinite circular cylinders in can touch pairwise. This answers a question of Littlewood from 1968. Fo…
math.MG2026
Insertion and expansion of cylinders around the unit ball
Ivan Matić, Radoš Radoičić, Andreas Spomer
A unit ball is surrounded with a ring of equal infinite circular cylinders. Each cylinder touches the ball and its two neighbors. Can one more cylinder of the same radius be ad…