Transformations in the Half-Plane Model

From the tools in the list below you can transformate points, segments, triangles and circles in the Half-Plane Model.

In the links below we explain how the tool were created. The macros can be downloaded from Hyperbolic_Isometries.gsp. To use them you need The Geometer Sketchpad software.

The transformations (isometries) in the Half-Plane Model are composition of inversions with respect to the hyperbolic lines (you can find some information about inversions and a macro which allows to plot the inversive point with respect to any circle in the plane). From the composition of inversions we can find: Moreover, at Half-Plane_Model2.gsp you can find the tool which allow to move a given segment to another position.

- Transport of segments.

Hyperbolic geometry

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