20.500.12556/RUL-84659 Routhov izrek diplomsko delo Routh's theorem V elementarni geometriji je eden najpomembnejših izrekov o geometriji trikotnikov Cevov izrek. Cevov izrek podaja kriterij, kdaj množica treh Cevovih premic, po ena skozi vsako oglišče in točko nasprotiležne stranice danega trikotnika, tvori šop. Routhov izrek je neke vrste posplošitev Cevovega izreka, saj v primeru, da dane Cevove premice ne tvorijo šopa, poda razmerje ploščin danega trikotnika in trikotnika, ki ga dobimo s presečišči Cevovih premic. V diplomskem delu predstavimo in dokažemo Routhov izrek s pomočjo Menelajevega izreka. V zadnjem delu diplomskega dela pa predstavimo še posplošitev Routhovega izreka za primer, ko imamo šest Cevovih premic, po en par premic skozi vsako oglišče danega trikotnika. The Ceva's theorem is one of the most important theorems in elementary geometry. This theorem provides criteria under which a set of three Ceva's line segments, one through each vertex and a point of opposite lying side of the given triangle are concurrent. The Routh's theorem is a kind of generalization of the Ceva's theorem. When the given Ceva's lines are not concurrent, the Routh's theorem gives the ratio between the areas of the given triangle and the triangle, which we get with the intersection of the Ceva's lines. In this work we present and prove the Routh's theorem with the help of the Menelauses' theorem. In the last part of this work we present the generalization of the Routh's theorem to the case when six Ceva's line segments are given, one pair through each vertex of the given triangle. trikotnik Cevov izrek ploščina trikotnika triangle true false false [M. Remic] Slovenski jezik Angleški jezik Diplomsko delo 2016-08-31 02:36:38 2016-09-09 16:48:27 2025-04-17 04:52:29 0000-00-00 00:00:00 2016 0 0 VIII, [60] str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514(043.2) 11120457 DIPLOMA_MR.pdf DIPLOMA_MR.pdf 1 DBEB1EE1C2E45C0000E03F85907653CF e9a6ada5ed977a229abb9f63c6779bb5c4f0ebc5112930fab3e0e9fbdb3ba885 6dea50d9-1aab-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=204680 Pedagoška fakulteta 0 0 0