20.500.12556/RUL-110745 Ponceletov izrek delo diplomskega seminarja Poncelet's theorem Ponceletov izrek pravi, da če za stožnici $S_1$ in $S_2$ obstaja $n$-kotnik, ki je včrtan stožnici $S_1$ in očrtan stožnici $S_2$, potem za $S_1$ in $S_2$ obstaja neskončno takih $n$-kotnikov. Vsaka točka na $S_1$ je oglišče kakega opisanega $n$-kotnika in vsaka točka na $S_2$ leži na stranici kakega opisanega $n$-kotnika. V realni projektivni ravnini najprej predstavimo in dokažemo poseben primer Ponceletovega izreka za trikotnike in nato še splošni izrek. Pri tem si pomagamo s Pascalovim izrekom, Brianchonovim izrekom, Carnotovim izrekom, dualom Carnotovega izreka in nekaj pomožnimi trditvami. Poncelet's theorem states, that if $n$-sided polygon is inscribed in conic $S_1$ and circumscribed about conic $S_2$, then there exists infinitely many of such polygons. Moreover, for any point $P$ of $S_1$, there exists an $n$-sided polygon, also inscribed in conic $S_1$ and circumscribed about conic $S_2$, which has $P$ as one of its vertices, and for any point $R$ of $S_2$, there exists an $n$-sided polygon, also inscribed in conic $S_1$ and circumscribed about conic $S_2$, such that tangent to $S_2$ from $R$ is one of its lines. In real projective plane we first explain special case of Poncelet's theorem for triangles and then the general case. For that we use Pascal's theorem, Brianchon's theorem, Carnot's theorem, dual of Carnot's theorem and some other claims. Ponceletov izrek projektivna geometrija stožnica Poncelet's theorem projective geometry conic true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2019-09-19 07:45:38 2019-09-19 07:45:42 2024-05-30 10:20:47 0000-00-00 00:00:00 2019 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514 99891 18821209 1074.pdf 1074.pdf 1 BE2DD1BF711B692AA3125425C63E563A dd0d2e5d9ff30cec0b285f2dadbeeb963c7d4136722a83bcf7902042026363a2 31d3130c-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122441 Fakulteta za matematiko in fiziko 0 0 0