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math.MG2025
Periodic double tilings of the plane
Francesco Nobili, Matteo Novaga, Emanuele Paolini
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e.,…
math.MG2024
On the total surface area of potato packings
Matteo Novaga, Emanuele Paolini, Eugene Stepanov
We prove that if we fill without gaps a bag with infinitely many potatoes, in such a way that they touch each other in few points, then the total surface area of the potatoes must…
math.MG2024
Steiner trees with infinitely many terminals on the sides of an angle
Danila Cherkashin, Emanuele Paolini, Yana Teplitskaya
The Euclidean Steiner problem is the problem of finding a set , with the shortest length, such that is connected, where is a given set in a Euclidean space. The…