Vilko Niče (1902. – 1987.)

Vilko Niče (Grubišno Polje, 1902 − Zagreb, 1987) was the most prominent geometrician synthesist 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’smethod 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 the sehyperboles describe a deltoid