Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1994. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 22)

SZILASSI, L., A computer-aided.démonstration of the Poincare model of hyperbolic geometry

A computer-aided démonstration of 133 that point of the Une (represented as an arc on the P-model), which is the closest to the origin O, lines passing through O were given by their normal vector. Using these parameters has proved to be advantageous especially when drawing pencils. Another procédure used many times is drawing the perpendicular bisector of a segment determined by two points of the hyperbolic plane on the Pmodel. It can easily be used to visualise the relation of the perp. bisectors of the sides of a triangle, about which, in absolute geometry, we can only prove that they belong to the same type of pencil. By demonstrating this, we can make students aware that when they prove in the school the theorem about the centre of the circle circumscribed to a triangle, they in fact accept the existence of the intersection of the two perp. bisectors as an équivalent form of the parallel axiom. ABC

, the regulär curve passing through its vertices, and the lines perpendicular to the curve and passing through the vertices. These six lines belong to the same pencil in each of the three cases. The carrier of this pencil is either a point O, or a direction V (point at infinity), or a line o. The second part of the programme demonstrates the three différent types of pencils of the hyperbolic plane and the family of regulär curves corresponding to them.