Whale’s Bubble Spiral: Angle-Controlled Parametric Curve

This example demonstrates a “whale-bubble” spiral visualization: an angle-driven process generates a winding, layered spiral curve that resembles rising bubbles. The key math ideas are parametric curve construction, using angles to control the geometric relationships, curve fitting to obtain a smooth spiral from sampled points, and Cartesian coordinate graphing. Construction (from the provided GeoGebra commands): Angle is used to define/measure the controlling angular relationships; Fit is applied to approximate a smooth curve based on constructed points; CurveCartesian is used to generate and display the curve in a Cartesian setting. Many point objects (e.g., A-, B- sets and their numbered variants) serve as discrete samples or intermediate construction points that feed into the spiral’s fitted curve. Suitable for high school through introductory university use in geometry construction, parametric equations, and mathematical visualization.