Found problems: 79
1951 Miklós Schweitzer, 16
Let $ \mathcal{F}$ be a surface which is simply covered by two systems of geodesics such that any two lines belonging to different systems form angles of the same opening. Prove that $ \mathcal{F}$ can be developed (that is, isometrically mapped) into the plane.
1966 Miklós Schweitzer, 1
Show that a segment of length $ h$ can go through or be tangent to at most $ 2\lfloor h/\sqrt{2}\rfloor\plus{}2$ nonoverlapping unit
spheres.
[i]L.Fejes-Toth, A. Heppes[/i]
1979 Miklós Schweitzer, 5
Give an example of ten different noncoplanar points $ P_1,\ldots ,P_5,Q_1,\ldots ,Q_5$ in $ 3$-space such that connecting each $ P_i$ to each $ Q_j$ by a rigid rod results in a rigid system.
[i]L. Lovasz[/i]
1983 Miklós Schweitzer, 4
For which cardinalities $ \kappa$ do antimetric spaces of cardinality $ \kappa$ exist?
$ (X,\varrho)$ is called an $ \textit{antimetric space}$ if $ X$ is a nonempty set, $ \varrho : X^2 \rightarrow [0,\infty)$ is a symmetric map, $ \varrho(x,y)\equal{}0$ holds iff $ x\equal{}y$, and for any three-element subset $ \{a_1,a_2,a_3 \}$ of $ X$ \[ \varrho(a_{1f},a_{2f})\plus{}\varrho(a_{2f},a_{3f}) < \varrho(a_{1f},a_{3f})\] holds for some permutation $ f$ of $ \{1,2,3 \}$.
[i]V. Totik[/i]