Dynamic Points and Limits in a Parallelogram (Q7)

①This example demonstrates the construction of a sequence of dynamic points within a parallelogram framework, observing their limiting positions and angle variations. ②Core mathematical concepts include parallelogram properties, vector translation and duplication, dynamic coordinates, sequences, limits, and angle measurement. ③Construction highlights: using GeoGebra commands such as Point, Vector, Sequence, DynamicCoordinates, Segment, Intersect, Polygon, If, and Angle, it creates base points A, B, C1, generates point sequences UPoints and VPoints via vectors u and v, duplicates vectors uCopy and vCopy to form parallel lines, finds intersections C and C', and constructs polygons with angle labels, possibly involving numerical limit approximation. ④Suitable for high school or early college students to intuitively grasp vector geometry, dynamic construction, and limit concepts, and can serve as material for mathematical experiments or inquiry-based learning.