# GeoGebra for modern physics

This is a proposal to create a GeoGebra Group in order to develop the resources to create a GeoGebra environment based on the pseudo-euclidean metrics of space-time.

The published GeoGebra package uses euclidean metrics as a general background, beginning with the 2D environment, followed by a 3D environment.These can be used to develop a lot of different geometric spaces (plane or curved ones), as well as to simulate the behaviour of non-euclidean geometries.

This idea is to begin with the implementation of the same general 2D Tools as in the existing euclidean version but using the pseudo-euclidean metric instead. Some of the Tools (such as Point, Midpoint, Intersect, Line, Segment, Vector, Parallel, Tangent, Polygons, Slope, Translation, Dilation) would remain unchanged, while others (like Perpendiculars, Angles, Bisectors, Polar line, Circles and Arcs, Distance, Reflections, Rotations) would be very slightly changed in their algebraic formulation (the main change being the introduction of a minus sign in certain places) but with striking geometric and visual differences (for example, the tool Circles would produce equilateral hyperbolas, which are the ubiquitous geometric structures of space-time).

The resulting 2D environment could be further complemented with a 3D environment with geometrical objects like the light cones showing their usefulness to understand the features of modern physics.

It should also be possible to produce specific tools to work with curved spacetimes, which would open the gate to explore the geometrical features of General Relativity.

You can read more about this topic HERE.

Xabier Prado

Wow. That would be spectacular, but maybe a really big job.

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