Rotation Exploration: Dynamic Angle and Geometry Interaction

① This GeoGebra example dynamically demonstrates how a point rotates around a fixed point, showing changes in angle, segment length, and figure position, making the fundamental geometric transformation of rotation intuitive. ② Core mathematical concepts include rotation (transformation), angle measurement, segment length, intersection points, and the role of trigonometric functions (sine, cosine) in rotation, with additional tags like arithmetic mean and binomial distribution as context, but the main focus is geometric rotation. ③ Construction highlights: Using GeoGebra commands such as Intersect (to find intersection points), Segment (to construct segments), Distance (to measure lengths), Point (to create points), and Angle (to mark angles), with objects A, B, f (possibly a function or curve), text1 (text display), distanceAB (length of segment AB), C (rotating point), g (another curve or segment), and α (rotation angle). By adjusting α via a slider or input, users observe dynamic changes in the figure. ④ Suitable for middle school (basic geometric transformations) and high school (trigonometry) mathematics classrooms, either for teacher demonstrations or student self-exploration, to understand properties of rotation, relationships between angles and distances, and the impact of parameter changes in dynamic geometry.