Vilko Niče (1902–1987)

Vilko Niče (Grubišno Polje, 1902. − 1987., Zagreb) najveći je geometričar-sintetičar 20. stoljeća u Hrvatskoj, ali i na području bivše SFRJ. Njegova biografija i bibliografija zainteresiranima je dostupna u pisanom i elektroničkom obliku te se ovdje ne navodi. U prvom dijelu članka dane su osnovne smjernice i upute o dostupnosti članaka o Ničeu kao osobi, ali i o dostupnosti njegovih znanstvenih radova i autorskih knjiga. Nadalje, članak se bavi subjektivnim impresijama o Ničeu kao znanstveniku, pedagogu, prijatelju, gospodinu. Sve svoje znanstvene radove Niče je obrađivao jedinstvenom, sintetičkom metodom i u tome ga još nitko nije nadmašio. S obzirom na metodu istraživanja, imao je mnogo sljedbenika u bivšoj državi, koje zovemo ničeovcima. U drugom i trećem teoremu, u drugom dijelu ovoga članka, najbolje se ilustrira Ničeova metoda u geometriji. Steinerova deltoida jedna je od najčešće obrađivanih ravninskih krivulja u geometriji. U ovom se članku sintetičkom i konstruktivnom metodom do nje dolazi na posve originalan način preko leptirovih teorema, koji se dovode u vezu s krivuljom središta u pramenu konika. Dokazuje se da je krivulja središta u pramenu ortogonalnih hiperbola kružnica te da sve asimptote tih hiperbola opisuju deltoidu.Vilko Niče (Grubišno Polje, 1902 − Zagreb, 1987) was the most prominent geometriciansynthesist of the twentieth century not only in Croatia, but also in the territory of the former Socialist Federative Republic of Yugoslavia. His biography and bibliography are available to interested audience in both written and electronic forms; hence, they are not mentioned here. The first part of the paper includes general guidelines and instructions regarding the availability of papers not only on Niče as person, but also on his scientific papers and books. The paper further deals with subjective impressions on Niče as scientist, pedagogue, friend, and gentleman. In all his scientific works, Niče applied a unique, synthetic method; he has remained unrivalled in this regard. Thanks to this research method, in the former state he had many followers, who were referred to as the ničeovci (followers of Niče). The second part of this paper – the second and the third theorem, illustrate best Niče’s method in geometry. Steiner’s deltoid is one of the most frequently treated plane curves in geometry. In this paper, by applying synthetic and constructive method, it is reached in an entirely original fashion via butterfly theorems, which are brought into connection with the curve of the centroids in the pencil of conics. It has been proved that the curve of the centroids in the pencil of orthogonal hyperboles is a circle, and that all the asymptotes of these hyperboles describe a deltoid