# 26 January 2021

## Proposal for a new command: ApplyMap

Last year I spent a couple of wonderful days in Madrid, right before the first lockdown of the COVID-19 pandemic. I visited my friends in Spain in the frame of an ERASMUS project. I also managed to meet Eugenio-Roanes Lozano, full professor of mathematics at the Department of Mathematics Education at Complutense University (or, more precisely at Depto. de Didactica de las Ciencias Experimentales, Sociales y Matematicas, Facultad de Educacion, Universidad Complutense de Madrid). Eugenio had an idea to extend GeoGebra with the following feature.

Given a planar construction with a couple of transformations, including reflections, rotations, translations or scaling. For example, for a given point $$P$$ a reflection about a line $$\ell$$ defines the point $$P'$$. Now, given another point $$Q$$ we may want to copy this transformation and obtain the point $$Q'$$ automatically.

By entering the command Q'=ApplyMap({P,P'},Q) we can obtain the sought point $$Q'$$. (Just copy-paste the command into the applet to give it a try.)

Note: This feature is in a prototype state. That is, it works only for reflections at the moment and it does not work reliably. Expect problems when using it.