Hyperbolic reflection
An inversion with respect to a hyperbolic line is called a hyperbolic
refection.
We can find the hyperbolic reflection of a point from the tools just
selecting two points of a hyperbolic line. To construct the tool for
obtaining the hyperbolic reflection of a point, we first plot the hyperbolic line and then we use the inversion tool to plot the image of the
point, that's to say, the hyperbolic reflection of the point.
The macro we have created allows also to reflect segments, triangles
and circles. To construct this other tools we just transform each of
the defining points and then we construct again the object from the
images points.
In the next figure it is plotted the reflection of a triangle
and a circle.
Note that the
reflection of an equidistant to the line reflection is the other
equidistant to the line reflection. We have the following:
Hyperbolic geometry
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