1. Kratka zgodovina perspektive in njene povezave z geometrijoJurij Kovič, 2026, strokovni članek Povzetek: V članku predstavimo primer obojestransko koristnega medsebojnega vpliva znanosti in umetnosti: kot je klasična Evklidova geometrija pomagala pri razvoju linearne perspektive v slikarstvu renesanse, je linearna perspektiva utrla pot opisni in projektivni geometriji. Perspektivo osvetlimo s teoretičnega, zgodovinskega, aplikativnega, učnega in pedagoškega vidika.
Ključne besede: matematika, zgodovina, perspektiva, geometrija
Objavljeno v DiRROS: 05.03.2026; Ogledov: 31; Prenosov: 14
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3. Platonic configurations of points and linesJurij Kovič, Aleksander Simonič, 2026, izvirni znanstveni članek Povzetek: We present some methods for constructing connected spatial geometric configurations $(p_q, n_k)$ of points and lines, preserved by the same isometries of Euclidean space $E^3$ as the predetermined Platonic solid. In this paper, we are mainly interested in configurations $(n_3)$, $(n_4)$, and $(n_5)$, but also in unbalanced configurations $(p_3, n_4)$, $(p_3, n_5)$, and $(p_4, n_5)$.
Ključne besede: configuration of points and lines, symmetry groups, Platonic solids, centrally symmetric solid, projection from a point
Objavljeno v DiRROS: 28.07.2025; Ogledov: 460; Prenosov: 229
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4. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, izvirni znanstveni članek Povzetek: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let $G$, $H$ be graphs and let $f: V(G) \to V(H)$ be a function. Then the Sierpiński product of graphs $G$ and $H$ with respect to $f$, denoted by $G\otimes_f H$, is defined as the graph on the vertex set $V(G) \times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $\{g, g'\}$ of $G$ there is an edge between copies $gH$ and $g'H$ of form $\{(g, f(g'), (g', f(g))\}$. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph $G\otimes_f H$ is connected if and only if both graphs $G$ and $H$ are connected and we present some conditions that $G, \, H$ must fulfill for $G\otimes_f H$ to be planar. As for symmetry properties, we show which automorphisms of $G$ and $H$ extend to automorphisms of $G\otimes_f H$. In several cases we can also describe the whole automorphism group of the graph $G\otimes_f H$. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation $n$ times to the same graph we obtain an alternative approach to the well-known $n$-th generalized Sierpiński graph.
Ključne besede: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Objavljeno v DiRROS: 19.03.2024; Ogledov: 1377; Prenosov: 841
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