Naslov
On improvements of the Butterfly theorem

Autori
Čerin, Zvonko ; Gianella, Gian Mario

Izvornik
Far east journal of mathematical sciences : FJMS (0972-0871) 20 (2006), 1; 69-85

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

Ključne riječi
quadrangle; butterfly theorem; conic; locus; nine-point-conic; cyclic quadrangle; Kiepert; Jarabek; Feuerbach; center; central point

Sažetak
This paper explores the locus of butterfly points of a quadrangle ABCD in the plane. These are the common midpoints of three segments formed from intersections of a butterfly line with the lines AB, CD, AD, BC, AC, and BD. The locus is the nine-point-conic of ABCD that goes through the midpoints of the segments AB, CD, AD, BC, AC, and BD. We also consider the problem to determine when two quadrangles share the nine-point-conic. Our proofs use analytic geometry of the rectangular Cartesian coordinates.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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