Rectangles in a Rectangle: Nested Rectangle Construction and Geometric Explorati

This example demonstrates how to construct multiple nested smaller rectangles inside a larger rectangle using perpendicular lines and intersection points, creating a hierarchical 'rectangles within a rectangle' structure. The core mathematical concepts include properties of rectangles, perpendicularity, intersection coordinates, and how dynamic slider adjustments affect the sizes and positions of the nested rectangles, involving coordinate geometry, translation transformations, and arithmetic operations. The construction uses GeoGebra commands such as Point, OrthogonalLine, Intersect, and Segment to create base points, perpendicular lines, intersections, and segments, then defines rectangle boundaries with objects like Rectangle, TopPoint, Vertical, RightPoint, Horizontal, and Concurrent, enhanced by a Slider and Reset button for interactive exploration. This is suitable for middle and high school students learning geometric construction, coordinate positioning, and dynamic geometry, and can also illustrate applications of LCM/GCD and logarithmic functions in parameter design.