TITLE:
A Methodology for Constructing and Verifying Solid Boundaries Using Parametric Surfaces in GeoGebra 3D
AUTHORS:
Rubi C. López-Sánchez, Jesús N. Zaragoza-Grifé, Caridad G. Vales-Pinzón, Gilberto A. Corona-Suarez
KEYWORDS:
Parametric Surfaces, Coordinate-Simple Solids, GeoGebra 3D, Multivariable Calculus, Triangulation, Mathematical Visualization
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.10,
October
30,
2026
ABSTRACT: This paper presents a manual construction protocol for boundaries of solids between two height functions over a planar region. It links inequalities, rectangular parameter domains, floor and roof lifts, and walls on actual contours. Boundary coverage is justified mathematically. Three original examples and eleven textbook exercises form a fourteen-case set whose methodological coverage and case-specific geometric acceptance conditions are explicit. According to consolidated author observations, all fourteen cases were opened, reconstructed from commands, inspected, saved, and reopened without incidents in GeoGebra Classic 6.0.920.0 on Windows 10 Home during September 3-15, 2026. No contemporaneous operation-level log or invariant-level inspection results were supplied. Fourteen screenshots, analytical integral checks, complete commands, and versioned construction files are provided; the supplement identifies the observations as retrospective. The contribution distinguishes actual contours from auxiliary partitions and seams, and positive-height joins from zero-height contacts. The reported 14/14 outcome applies only to the declared set and environment; it establishes neither independent reproduction nor educational effectiveness. The explicit protocol supports separately documented replay and future classroom evaluation.