Sine Light on a Golden Spiral

This example demonstrates how to impose a sine-wave modulation onto a golden-spiral parameter track, producing a visually “lit” ribbon whose highlights follow periodic trigonometric variation along the spiral. The key mathematics includes the golden-spiral/golden ratio parameterization, the periodic nature of the sine function, and modeling function values as a parameter-driven geometric construction. The construction uses GeoGebra commands and objects such as Sequence and CurveCartesian to generate parameter points and then trace the resulting curve. It introduces parameters (phi, t, n) to step through the spiral, constructs intermediate point objects (p, P) and derived quantities (including a sine-related function like Ft), and controls the animation/appearance with variables such as speed, thickness, colors, and reset/run toggles (buttReset, run). Suitable for secondary school through early university audiences, especially for lessons on parametric curves, trigonometry, and dynamic geometric visualization.