Interactive Demonstration of the Parallel Axis Theorem

① This example visually demonstrates the parallel axis theorem using a draggable polygon: the moment of inertia about any axis equals the moment of inertia about a parallel axis through the centroid plus the product of the area and the square of the distance between the axes. ② Core mathematical concepts include moment of inertia (second moment of area), centroid, parallel axis theorem, and radius of gyration. ③ Construction details: a polygon is created with the Polygon command, the centroid is computed using Centroid, axes and distances are shown via Vector and Locus, conditional display is handled with If, and numerical values such as Area, I_{x Centroid}, I_{x Axis}, Gyration, and I_x are calculated and updated dynamically with buttons and text boxes. ④ Suitable for high school physics or university engineering mechanics students learning about moments of inertia, as well as for mathematics classes exploring area moments and geometric properties.