20.500.12556/RUL-171997 Caseyjev izrek delo diplomskega seminarja Casey’s theorem V diplomski nalogi bomo formulirali in dokazali Caseyjev izrek o tangentnosti štirih krožnic na peto ter nekatere njegove posledice. Za lažje razumevanje bomo začeli s Ptolemajevim izrekom, ki govori o tetivnem štirikotniku in je poseben primer Caseyjevega. V nadaljevanju bomo definirali tangente med krožnicami in njihove lastnosti, nato pa si bomo pogledali Caseyjev izrek. Pred dokazom inverza izreka, bomo definirali tudi, kaj je inverzija in kako slika objekte v ravnini. In this thesis, we will formulate and prove Casey’s theorem on the tangency of four circles to a fifth, as well as some of its consequences. For easier understanding, we will start with Ptolemy’s theorem, which deals with the chord quadrilateral and is a special case of Casey’s. We will define the tangents between circles and their properties, and then we will look at Casey’s theorem. Before proving the inverse of the theorem, we will also define what an inversion is and how it maps objects in a plane. We will conclude the thesis with a demonstration of some of the consequences. Caseyjev izrek tangentne krožnice inverzija potenca točke na krožnico podobnost Casey’s theorem tangent circles inversion the power of a point similarity true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-09-05 08:15:17 2025-09-05 08:15:19 2025-09-30 03:41:26 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514 152602 247862787 18943.pdf 18943.pdf 1 53568042D1FE8A00413B419FEC891FDB 0e31c1bb3529e8600120bcf70b33e4bfaa20e3e921a1ae3c37afea8460d76b64 8c65d952-8a1f-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=215715 Fakulteta za matematiko in fiziko 0 0 0