Positive Curvature: Sphere and Exponential Surface Construction

This GeoGebra example illustrates a surface with positive curvature by combining a sphere and exponential functions, demonstrating how curvature remains positive across the surface. The core mathematical concepts involve curvature, spherical geometry, exponential and quadratic functions, as well as intersections, tangents, and derivatives. The construction uses commands such as Intersect to find intersection points between surfaces and curves, Surface to generate 3D surfaces, PointIn to place points on objects, and CircleArc to draw arcs. Key objects include sphere c, point A, intersection i, point B, arc a, points D, C, F, E, and curves d, e, f. This example is ideal for high school and university students learning geometry and calculus, offering a visual and interactive way to understand positive curvature and practice using dynamic 3D geometry tools.