Naslov
Eine neue Schmetterlingskurve
(A generalization of the butterfly curve theorem)

Autori
Sliepčević, Ana

Izvornik
Mathematica Pannonica (0865-2090) 16 (2005), 1; 57-64

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Schmetterlingspunkt; Schmetterlingsgerade; Schmetterlingskurve; KS-Bueschel
(butterfly line; butterfly point; butterfly curve; pencil of conics)

Sažetak
It is shown how for each "butterfly figure", inscribed in any conic a point with the butterfly property can be constructed in the arbitrary direction. It is proved that all such points associated to particular butterfly lie on a conic. This conic is also the curve of central points of the pencil of conics determined by the butterfly figure. Further, it is proved that the set of all the lines made of butterfly's points associated to a butterfly figure inscribed in a circle wraps a curve of the 4th order the 3rd class. Such a curve is constructed.

Izvorni jezik
Ger

Znanstvena područja
Matematika

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