Limit Visualization of a Sum Puzzle via Geometric Splitting

This GeoGebra example demonstrates how a “sum puzzle” can be visualized by repeatedly splitting geometry into segments and accumulating the resulting pieces. By iterating (often with animation), the construction reveals a limiting behavior: as the number of subdivisions grows, the total value approaches a stable result. Key math concepts include rational-number proportions, triangle/polygon geometry, and the idea of limits as a bridge between discrete sums and a continuous outcome. Construction highlights: it uses Line, Point, and Ray to set up reference lines and key points; Segment and Polygon to build and combine triangular or polygonal regions; Mod to manage periodic or step-dependent indexing; If to switch between conditional construction rules; and Increment (with parameters/iterators like t, i, T1 and many generated objects) to drive the iterative generation of new faces/parts (e.g., stored in objects such as poly1 and related variables). Suitable for upper-secondary students through early university, for math-visualization activities, classroom demonstrations, and explorations introducing limits through geometric summation.