Surface of a Two-Variable Function via Geometric Construction

This example visualizes the 3D graph (surface) of a two-variable function z = g(x, y) while integrating triangle-related geometric figures—highlighting relationships connected to the incircle, and contrasting right triangles and equilateral triangles within the same visual setup. The key mathematical ideas include multivariable functions and function graphs (surfaces), geometric construction/transform visualization, and triangle-geometry concepts tied to the incircle. Construction approach in GeoGebra: the Surface command builds the surface from an object f (the function definition), while Point and multiple labeled text objects (text1–text6) create and annotate critical points A, B, C, D, E and related point b, ensuring the geometry and the surface are presented together for interpretation. Suitable for upper-secondary through early university contexts, especially lessons on coordinate/analytic geometry, graphing multivariable functions, and geometry-based visualization/modeling.