Geometric Mapping of Real Numbers onto the Unit Circle

This GeoGebra example demonstrates the geometric mapping of real numbers from the real line onto the unit circle, creating a visual one-to-one correspondence. The core mathematical concepts involved include real numbers, the unit circle, trigonometric mappings, right triangles, similar triangles, and geometric means. Key construction points feature the use of GeoGebra commands such as Circle, Intersect, Rotate, Angle, Tangent, CircleArc, Segment, Center, and AngularBisector, dynamically manipulating objects like O, A, c, t, θ, B', β, P to trace the mapping trajectory. This resource is ideal for high school and college-level students studying trigonometry, analytic geometry, and mathematical analysis, providing an intuitive understanding of continuous mappings.