0202 Tools in the P-model
Basic editing tools on the P-model
We ask our readers to use the slider to explore the possibilities of our toolbox, and to carefully study the resulting hyperbolic - and at the same time absolute - geometric objects by moving the base points. Repeat the same edits on your own computer with the already downloaded Geogebra program. Later, use this - downloaded - toolbox for your own edits.
20201
Our readers have probably noticed that all the drawing commands have disappeared from the GeoGebra icons. Even the point pick-up. This is no coincidence. We had to ensure that the base points that form the basis of the edits are only the points of the modeled Hyperbolic plane, i.e. they remain within the base circle of the model even when moved. Therefore, we eliminated the inclusion of so-called flying points. This means that if we need to enter a point as input data for a shape, we cannot get it in the usual way by clicking on an empty space. The button in the upper left corner of the drawing page, which generates the base points of the procedure, always places the newly added points in the center of the base circle, so they must be dragged from there with the mouse. We hope that the use of the tools can be learned without analyzing each one separately. However, we note that the P-model's HExline[] and HCircle[] tools correspond to the two basic tools of Euclidean construction suitable for drawing. However, we can state that all of the procedures presented here, e.g. HMetric[] or HSegmentBisector[] can also be traced back to basic Euclidean constructions, therefore these procedures can also be considered - in a broader sense - as Euclidean constructions. The latter would have been more appropriate (and shorter) to call it HMirrorAxis[] , but we tried to follow the "official" terminology of GeoGebra. The HIntersection1[] method is suitable for recording the intersection point of two H-segments, H-half-lines or H-lines. (Although two circular arcs can have up to two common points, it is clear that two H-lines have at most one common point.) The HIntersection2[] is used to record the intersection point of two H-segments, H -half-lines or H-lines. can be used to record the intersection of a ray, but only if the editing is clear. That is, if one of the endpoints of the segment or the starting point of the ray is inside the circle. If we are looking for the intersection of an H-circle and an H-line, or both intersections of two H-circles , then – but only then – we enter the GeoGebra Intersection[] command in the command line. For example, in the experiment below, the intersections of the H-circle c and the H-segment d were entered with the GeoGebra Intersection[c,d] command. Here, the two intersections are distinguished not only by their names, but also by their colors.