293 KB0 KB200820262023Razpet, Markoštevilka:4letnik:70str. 121-131ISSN:0473-7466COBISSID_HOST:188212995URN:URN:NBN:SI:doc-XG9N6CD9slDruštvo matematikov, fizikov in astronomov SlovenijeObzornik za matematiko in fizikoFilonova premicageometrijageometryPhilon lineFilonova premica|The Philon line through a selected point inside a given angle intersects its two arms in such a way that the distance between the intersections is the shortest. In general, the geometric construction of a Philon line is not possible only with an unlabelled ruler and pair of compasses. The problem leads to a cubic equation, whose only positive root exactly determines the Philon line. We will explain its main properties. The Philon line is also obtained by the intersection of a circle and a hyperbolaFilonova premica skozi izbrano točko v notranjosti danega kota seka njegova kraka tako, da je razdalja med presečiščema najmanjša. Geometrijska konstrukcija Filonove premice na splošno ni mogoča samo z neoznačenim ravnilom in šestilom. Problem vodi do kubične enačbe, katere edini pozitivni koren natančno določa Filonovo premico. Pojasnili bomo njene glavne lastnosti. Do Filonove premice pridemo tudi s presečiščem krožnice in hiperboleTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaDruštvo matematikov, fizikov in astronomov