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
2022-10-14 09:33:32
0000-00-00 00:00:00
2019
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0
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NiDoloceno
NiDoloceno
NiDoloceno
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514
99891
18821209
1074.pdf
1074.pdf
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https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122441
Fakulteta za matematiko in fiziko
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