||From Static Locus Problems to Exploring Mathematics with Technological Tools
This is an expanded version of an earlier paper. We discuss two problems taken from practice problems preparation guides for entrance examinations into Chinese universities. We see how original problems in 2D, stated in an exam static and uninspired settings, can be extended to other interesting cases in 2D and more challenging corresponding problems in 3D for students to explore with the help of a Dynamic Geometry Software (DGS) and a Computer Algebra System (CAS). We use a DGS to construct the locus or locus surface geometrically, and use a CAS to verify our locus or locus surface analytically. We shall see that with the innovative use of technological tools, mathematics can be made more fun, accessible, challenging and applicable to a broader group of students and teachers alike. Finally, we attempt to make these problems relevant to real-life applications, and invite readers to imagine some other interpretations for the proposed situations. A video clip summarizing those examples using GInMA can be found in a reference given in the paper.