3D Implicit Surface Grapher: Goursat's Surface

This interactive GeoGebra example demonstrates the graphing of 3D implicit surfaces, with a focus on Goursat's surface, a classic algebraic surface. Core mathematical concepts include implicit equations, 3D parameterization, polynomial functions, and surface geometry. Construction highlights: using GeoGebra's text fields (Textfield) and buttons (button), the applet predefines 14 algebraic and 14 polynomial functions for selection; sliders (dx2, dy2, dz2) adjust the plotting ranges (x_min, x_max, y_min, y_max, z_min, z_max) and update the surface in real time; objects include function definitions (Funktion), color selection (Farbe), and multiple text labels (text1, text2, etc.) for interface guidance. Suitable for high school to university-level mathematics education, this tool helps students intuitively understand implicit surfaces, polynomial equations, and 3D visualization, and can be used to explore the topology and symmetry of special surfaces like Goursat's surface.