Elementarne konstrukcije konika u hiperboličnoj i eliptičnoj ravnini

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Elementarne konstrukcije konika u hiperboličnoj i eliptičnoj ravnini

Weiss, Gunter

KoG, 01/2016, Volume: 19., Issue: 19.

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U Euklidskoj ravnini poznate su konstrukcije točaka i tangenata za npr. elipsu c zadanu osima, pri čemu se koristi Apolonijeva definicija za c preko fokusa ili dva afiniteta (de la Hireova konstrukcija). Iako ne postoje paralelne relacije s hiperboličnom niti eliptičnom ravninom, ipak je moguće modificirati mnoge elementarne konstrukcije vezane za konike tako da one vrijede za (regularne) neeuklidske ravnine. U nekim modikacijama samo je euklidski pravac zamijenjen s neeuklidskom kružnicom. Također će se proučiti svojstva Talesovih konika koje su generirane s dva pramena (neeuklidskih) okomitih pravaca.

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