The upper dial-plate of the astronomical clock is an astrolabe controlled by a clockwork mechanism. It represents a stereographic projection of the celestial sphere from its North Pole onto the tangent plane passing through the South Pole. We give a survey of several astronomical mistakes that appeared on this dial throughout centuries., V letošním roce je orloji na Staroměstském náměstí v Praze právě 600 let. Před rokem 1979 byla na jeho astronomickém ciferníku nesprávně zakreslena kruhová oblast astronomické noci. V tomto článku se zmíníme o dalších významných kružnicích, jejichž rozměry a umístění na orloji by se daly ještě zlepšit., Michal Křížek, Pavel Křížek, Jakub Šolc., and Obsahuje bibliografii
Let f : I → X be a delta-convex mapping, where I ⊂ R is an open interval and X a Banach space. Let Cf be the set of critical points of f. We prove that f(Cf ) has zero 1/2-dimensional Hausdorff measure.
W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let $E/E^{\prime }$ be a 1-parameter closed planar Euclidean motion with the rotation number $\nu $ and the period $T$. Under the motion $E/E^{\prime }$, let two points $A = (0, 0)$, $B = (a + b, 0) \in E$ trace the curves $k_A, k_B \subset E^{\prime }$ and let $F_A, F_B$ be their orbit areas, respectively. If $F_X$ is the orbit area of the orbit curve $k$ of the point $X = (a, 0)$ which is collinear with points $A$ and $B$ then \[ F_X = {[aF_B + bF_A] \over a + b} - \pi \nu a b. \] In this paper, under the 1-parameter closed planar homothetic motion with the homothetic scale $ h = h (t)$, the generalization given above by W. Blaschke and H. R. Müller is expressed and \[ F_X = {[aF_B + bF_A]\over a + b} - h^2 (t_0) \pi \nu a b, \] is obtained, where $\exists t_0 \in [0, T]$.