Achievements and Challenges in Automatic Locus and Envelope Animations in Dynamic Geometry

Zoltán Kovács

doi:10.1007/s11786-018-0390-0

Abstract

A survey on the speed of real-time animation of loci and envelopes in the dynamic geometry software GeoGebra is presented.

Highlights

Dynamic geometry experiments on loci and envelopes may be fruitful activities in learning and research contexts
In the paper [14] we reported that non-trivial locus and envelope animations can be performed quickly enough by using today’s computers with implicit computer algebra use
It is remarked that the obtained data is a result of continuous improvements of many “ingredients” of the underlying system, including GeoGebra, its embedded computer algebra system Giac, and the construction steps that describe the mathematical content in a faster way than in some earlier attempts

Summary

Introduction

Dynamic geometry experiments on loci and envelopes may be fruitful activities in learning and research contexts. Six examples were shown in [14] in details when benchmarking them in four different computer algebra systems In this technical paper we continue investigating the computation speed in three systems, all used directly in the dynamic mathematics tool GeoGebra [12]. It is remarked that the obtained data is a result of continuous improvements of many “ingredients” of the underlying system, including GeoGebra, its embedded computer algebra system Giac, and the construction steps that describe the mathematical content in a faster way than in some earlier attempts In this sense the focus is on measuring if the assembled parts of the investigated system is capable of supporting classroom and research use of animating locus and envelope curves.

The Benchmarking System

The Database

An Example

Conclusion and Future Work