Vilko Niče (1902. – 1987.) Sliepčević, Ana
Radovi Zavoda za znanstvenoistraživački i umjetnički rad u Bjelovaru,
2016, Letnik:
10, Številka:
10
Journal Article
Recenzirano
Odprti dostop
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
Kvazieliptička ravnina jedna je od devet projektivno-metričkih ravnina. Apsolutnu figuru F_{QE} = { j_1; j_2;F} određuju dva imaginarna pravca j_1 i j_2 i njihovo realno sjecište F.
U ovom radu ...definirat ćemo osnovne pojmove, prikazati odabrane konstrukcije i dokazati jedan teorem.
The article observes a one-parameter triangle family T . We prove that
the sets of the orthocenters, centroids, circumcenters and the midpoints of the variable
triangle side of the triangle family T ...lie on four different hyperbolae. Furthermore,
there is constructed an envelope k_3^4 of the perpendicular bisectors of the variable triangle
sides. Also it is constructed a bicircular rational quartic as an envelope of the
circumcircles of the triangle family T.
Up till now the validity of the Butterfly theorem has been verified in
the Euclidean, isotropic, hyperbolic and pseudo-Euclidean plane. Furthermore, it
has been shown that an infinite number of ...butterfly points, located on a conic, is
associated with any quadrangle inscribed into a circle.
In the present paper we study the curve formed by butterfly lines. In the Euclidean
plane this curve is always a curve of order four and class three having one
real cusp while in the pseudo-Euclidean plane it can also be a curve of order four and
class three having three real cusps or a special parabola.
O nekim familijama trokuta Kovačević, Nikolina; Sliepčević, Ana
KoG,
01/2013, Letnik:
16., Številka:
16.
Paper
Odprti dostop
U ovom radu proučava se skup T ={T_(r,d): d ∈ R} specijalnih jednoparametarskih familija trokuta. Analizirat će se i opisati krivulje mjesta nekih točaka trokuta unutar danog skupa.
Koristeći činjenice teorije konika, dokazuju se dva teorema koji su analogoni klasičnih teorema geometrije trokuta. Za pramen parabola zadan trima temeljnim tangentama a, b, c dokazuje se da tjemene ...tangente svih parabola omataju deltoidu δ, a osi parabola u istom pramenu deltoidu α. Pokazuje se da su deltoide homotetične. Još se dokazuje da sva tjemena parabola u istom pramenu leže na krivulji 4. reda. Spomenute krivulje se konstruiraju i istražuju metodama sintetičke geometrije.
Sve perspektivne kolineacije u realnoj afinoj ravnini klasificiraju se s obzirom na karakterističnu konstantu te položaj središta i osi. Pokazuje se, kako odabrati temeljne elemente perspektivne ...kolineacije kako bi se neka konika i njezina slika dodirivale u jednoj ili dvije točke, oskulirale se ili hiperoskulirale. Na afinim se modelima izotropne i pseudoeuklidske ravnine pomoću perspektivne kolineacije konstruiraju oskulacijske kružnice konika.
Dobro su poznata svojstva krivulje euklidske ravnine zvane Pascalov puž. U ovom se radu u hiperboličkoj ravnini konstruiraju krivulje sa sličnim svojstvima. Te su krivulje nazvane hiperboličkim ...puževima i definirane kao nožišne krivulje kružnica.
Pokazuje se da su svi hiperbolički puževi cirkularne kvartike, a neke od njih su čak potpuno cirkularne.
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