Geogebra

This proposal has been posted at the GeoGebra Forum

See below some examples of the application of the same procedure in both plane metrics.

Dragging the vertexes of the triangles it is possible to recognise the striking similarities between the Euclidean property and its Minkowskian counterpart, where the perpendiculars are reflections about the diagonals and the circles are substituted by equilateral hyperbolas.

But the main geometric facts are preserved:

The fact that the Euler Line joins the three notable points (Circumcentre, Centroid and Orthocentre) in both cases, and, also, the fact that there are in both cases 9 points (constructed with the corresponding tools which render very different results) lying on a common "circle" (in the Minkowskian plane, the circle is substituted by a equilateral hyperbola).

To follow the construction process for these applets and have a look at the GeoGebra Environment for spacetime physics click HERE.