Monkey Saddle 3D Surface Demonstration

①This example demonstrates the geometric shape of the Monkey Saddle, a special 3D surface resembling a saddle for a monkey, featuring three saddle points instead of the usual two. ②The core mathematical concept is the graph of the multivariable function z = x³ - 3xy², relating to saddle point theory, partial derivatives, critical points, and local surface curvature. ③Construction: Based on the summary, only the object f (the defining function) is used; in GeoGebra, one inputs the function expression and enables the 3D view to generate the surface, possibly adjusting coloring or viewpoint to highlight saddle features. ④Suitable for advanced high school or early university courses in calculus, multivariable functions, and solid geometry, providing an intuitive visualization of saddle points and surface concavity, also useful for mathematical modeling or introductory computer graphics.