Mathematics education often faces the challenge of transforming abstract concepts into concrete experiences. Understanding hyperbolas and hyperboloids requires overcoming the barrier between two-dimensional imagination and three-dimensional cognition. Modern interactive technology offers an innovative solution—creating multi-layered cognitive paths through a combination of physical manipulation and digital simulation. Our "Hyperbolic Gap" exhibit is a practical application of this concept, constructing a complete mathematical exploration field within a 3-meter square space. Within this meticulously designed cubic space, visitors can simultaneously engage in two types of exploration: in the physical manipulation area, they can personally verify the geometric relationship between a straight rod and a hyperbola by rotating handles and adjusting the angle; in the digital interactive area, they can control parameters via a touchscreen and observe the dynamic surface changes formed.
