Vector Geometry with Rotation/Angle Control and Sketching Demo

This example demonstrates an interactive geometry sketch driven by rotation and angle constraints: vectors, circles, and polygonal elements are constructed and transformed so that geometric relationships become visible curves and ratio-based relations. Key math concepts include 2D vectors, angle-dependent rotation, construction of circles/segments/polygons, and conditional (if) logic to select or build the appropriate parts of the diagram. The original theme also suggests links to arithmetic and probability/statistics topics such as Poisson distribution within the lesson workflow. Construction highlights in GeoGebra: Rotate is used to rotate objects around a pivot; Angle provides or measures the controlling angle parameter; If implements conditional construction; Segment, Circle, and Polygon create the fundamental geometric primitives; Sequence supports iterative sampling or stepping through parameters; Vector defines directional quantities; and multiple points/variables (e.g., vectors and labeled points like A, P, α, and collections of objects such as B–M), together with lists (list1, list2, list3, list4, list6) and buttons (button1, button2), enable a guided step-by-step or batch generation of the sketch. Suitable for secondary school through early university audiences, for geometry construction, coordinate-geometry visualization, and classroom demonstrations that connect parameters, transformations, and curve sketching.