Implementing continuation homotopy typically relies on numerical techniques such as Newton–Raphson iteration, Euler prediction, and interpolation. As the size or nonlinearity of the system of equations increases, the computational demands escalate, necessitating workstations with ample RAM, high-performance processors, and software environments like Maple, MATLAB, Fortran 90, or C++. This study explores a low-cost alternative: a scalar implementation of hy-perspherical tracking on the 8-bit PIC18F4620 microcontroller—hardware that lacks a mathe-matical coprocessor and the resources of a conventional PC. The algorithm, written in MikroC, drives a 128 × 64-pixel monochrome graphic display that plots the homotopy trajectory and marks the converged root. Four case studies demonstrate that, despite the display’s limited resolution, the root error can be maintained below 10⁻⁶. These results confirm that advanced homotopy concepts can be realized on modest hardware, providing a practical teaching tool for courses that integrate microcontroller programming with numerical analysis.
The article outlines two instructional pathways. The first targets undergraduate engineering courses, where students already have a foundation in numerical methods and embedded C. The second is tailored to technology-oriented baccalaureate programs, adopting a STEM (Pantoja-Amaro, 2020) perspective to highlight the real-world relevance of mathematics. Both pathways emphasize interdisciplinary learning: students connect algebra, analytic geometry, and differen-tial calculus to hands-on electronics, deepening their understanding while developing transfera-ble engineering skills.
Keywords: PIC microcontroller, homotopy continuation with spherical tracking, school mathematics speech, numerical analysis, educational mathematics.
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