Poincaré disk

The Poincaré disk is a model that allows us to play with Hyperbolic Geometry, a non-Euclidean geometry in which two similar figures, with the same shape, even have the same dimensions, they are exactly the same and, having fixed a point and a straight line, there are infinitely many straight lines which pass through that point and do not cross that straight line. In this model the points are the points inside the disk (the circumference is as if it were infinitely far away and its points are not points of the model). Straight lines are diameters of the disk or arcs of circles which form right angles with the circumference which is the boundary of the disk.

Click & drag to add a point and then (by dragging) a second point and the line joining them (second button from the left). Two lines can share the same point.

The third button allows you to draw the two straight lines that pass through an assigned point and are parallel to a given straight line (which means they have in common with this straight line a point on the circumference which is the edge of the model): click near the chosen straight line and then drag to place the point outside the line where you want.

The fourth button allows you to draw a freehand drawing. 

The fifth button allows you to add straight lines which act as “mirrors” and reflect the drawing made.

Finally, the arrow tool (first button on the left) allows you to move the points and consequently the lines that pass through those points. You can also move the line by clicking & dragging on the arc.

The animation derives from a suggestion by Silvia Maria Carla Pagani (who has no responsibility for any inaccuracies or defects). The source code is freely available at https://github.com/gianmarco-todesco/poincare-disk.

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