A Peculiarity of the Helix Tangent

This GeoGebra example demonstrates a peculiar geometric property of the tangent line to a cylindrical helix in 3D space. It visualizes how the tangent direction relates to the helix's parameterization and reveals an interesting locus. Core mathematical concepts include space curves, tangent lines, cylindrical surfaces, parametric equations, intersections of planes and surfaces, and locus generation. The construction uses commands such as CurveCartesian to define the helix, Point to place a point on the curve, Tangent to draw the tangent at that point, Plane and Intersect to create auxiliary planes and find intersections, Locus to trace moving points, and Surface to render the cylinder. Objects include a, A, b, B, C, D, c, E, loc1, d, e, m, R, f, g. This resource is suitable for high school or university courses in analytic geometry or calculus, helping students intuitively grasp the changing direction of tangents to space curves and their geometric implications.