On Euler's inequality and automated reasoning with dynamic geometry

Euler's inequality $R\geq 2r$ can be investigated in a novel way by using implicit loci in GeoGebra. Some unavoidable side effects of the implicit locus computation introduce unexpected algebraic curves. By using a mixture of symbolic and numerical methods a possible approach is sketched up to investigate the situation. By exploiting fast GPU computations, a web application written in CindyJS helps in understanding the situation even better.

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