Antal Jo'os

activity

20212023

most citedIsoperimetric problems for zonotopes

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.MG2023

Covering the Crosspolytope with Crosspolytopes

Antal Joós

Let $γ_{m}^{d} (K)$ be the smallest positive number $λ$ such that the convex body $K$ can be covered by $m$ translates of $λ K$ . Let $K^{d}$ be the $d$ -dimensional crosspolytope. It will b…

math.CO2022

Perfect packing of squares

Antal Joós

It is known that $i = 1 \sum \infty 1/ i^{2} = π^{2} /6$ . Meir and Moser asked what is the smallest $ε$ such that all the squares of sides of length $1$ , $1/2$ , $1/3$ , $\ldots…

math.CO2022

Packing $1.35 \cdot 1 0^{11}$ rectangles into a unit square

Mingliang Zhu, Antal Joós

It is known that $i = 1 \sum \infty \frac{1}{i ( i + 1 )} = 1$ . In 1968, Meir and Moser asked for finding the smallest $ε$ such that all the rectangles of sizes $1/i \times 1/…

math.MG2022★ 1 cited

Isoperimetric problems for zonotopes

Antal Joós, Zsolt Lángi

Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this…

math.MG2021

Cubes and Boxes have Rupert's passages in every direction

András Bezdek, Zhenyue Guan, Mihály Hujter +1

It is a $300$ year old counterintuitive observation of Prince Rupert of Rhine that in cube a straight tunnel can be cut, through which a second congruent cube can be passed. Hundre…