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 conipinor-aiílrtl tU-moiiM ral ion of 137 p" P = t n / The other one: we determine the point P 1 corresponding to x on the axis Ä" , the we choose the point P on the line containing P' and perpendicular to A" (the locus of points with the same abscissa) for which the length of P 1 P is //. =>P' G .Y => € f i A" r e P' =>P = P e f. PP' = ij In Euclidean geometry the rectangle 0 F' P P" has the properties which make these two constructions équivalent. However, this is différent in hyperbolic geometry. If we chose the first way, it may very well happen that the lines perpendicular to the axes do not intersect, if the reals x, y are big enough. Choosing the other way, on the other hand, the locus of points with given ordinate —i.e. points from the same distance from the axis À" — will be a hypercycle. This is how we obtain the lattice we saw when demonstrating ultrapara.
