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-aiileil <lemonM ration of 139 where q = Ln \j —-—- . V r - k 4. The graph of functions on the P-model As a resuit, we have drawn the graph of a few well known functions (y = x\ y — .r

2; y — 2' ; y — log

2(j'); y = -, in this system of coordinates. We réalisé that the extent to which these graphs approach their usual shape depends on the ratio of the radius of the circle of inversion and the unit. The figures show the cases ^ » 0,1, ^ a 0.3, ^ % 0.04. In the last one the graph is very close to its usual form near the origin. The user of the programme can réalisé that fixing k and increasing r, the model approaches the Cartesian system of Euclidean geometry. Choosing r big enough, we cannot feel the différence on the screen, just as we cannot feel sitting in a room that the Earth is a sphere.