engleski

The Butterfly Theorems in the Hyperbolic Plane

There are many varieties of Butterfly Theorem in the Euclidean plane. Here some analogous theorems in the hyperbolic plane are proved. It is shown that proofs do not depend on the class of circle into which complete quadrangle is inscribed. The only difference is between the case when qadrangle is inscribed into absolute conic and the case when it is inscribed into one of three classes of circles. The construction of the points with butterfly property is given. It is proved that with any quadrangle an infinite number of butterfly points is associated which are located on a second order curve.

Butterfly Theorem; hyperbolic plane

nije evidentirano