M. Lassak

activity

20162022

most citedWhen a spherical body of constant diameter is of constant width?

1 citations · 2 across the 5 of their papers we have counts for

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math.MG2021

Approximation of Spherical Bodies of Constant Width and Reduced Bodies

Marek Lassak

We present a spherical version of the theorem of Blaschke that every body of constant width $w < \frac{π}{2}$ can be approximated as well as we wish in the sense of the Hausdorff dis…

math.MG2021

A note on some generalizations of Monge's theorem

Marek Lassak

We generalize Monge's theorem for $n + 1$ pairwise homothetic sets (in particular convex bodies) in $E^{n}$ in place of three disks in $E^{2}$ . We also present a version for $n + 1$ indepe…

math.MG2020

Spherical geometry -- a survey on width and thickness of convex bodies

Marek Lassak

We present a survey article about the geometry of convex bodies on the $d$ -dimensional sphere $S^{d}$ . We concentrate on the results based on the notion of the width of a convex body…

math.MG2020

Banach-Mazur distances between parallelograms and other affinely regular even-gons

Marek Lassak

We show that the Banach-Mazur distance between the parallelogram and the affine-regular hexagon is $\frac{3}{2}$ and we conclude that the diameter of the family of centrally-symmet…

math.MG2020

Complete Spherical Convex Bodies

Marek Lassak

Similarly to the classic notion in $E^{d}$ , a subset of a positive diameter below $\frac{π}{2}$ of a hemisphere of the sphere $S^{d}$ is called complete, provided adding any extra point…

math.MG2019★ 1 cited

When a spherical body of constant diameter is of constant width?

Marek Lassak

{\bf Abstract.} Let $D$ be a convex body of diameter $δ$ , where $0 < δ < \frac{π}{2}$ , on the $d$ -dimensional sphere. We prove that $D$ is of constant diameter $δ$ if and only if it i…