Rolling of a Reuleaux Rotor on an Equilateral Triangle with Variable Side Length

This GeoGebra example demonstrates the rolling motion of a Reuleaux triangle, a classic curve of constant width, as it rotates inside an equilateral triangle with an adjustable side length. By dragging a slider, users can vary the triangle's side length and observe how the Reuleaux rotor rolls smoothly along the interior sides while maintaining continuous contact. The construction builds the Reuleaux triangle using circumcircle arcs and then applies rotation, translation, and sequence commands to animate the rolling path. As the rotor rolls, its orientation shifts dynamically, tracing out a轨迹 that reveals the remarkable geometric relationship between this equal-width curve and the enclosing equilateral triangle. This interactive exploration highlights the unique property of constant-width curves: despite their non-circular appearance, they roll with a smooth, steady motion akin to a circle. Students benefit from this visualization by gaining an intuitive understanding of rotation transformations, locus generation, and parametric animation. They can experiment with different triangle sizes to discover how the rolling behavior adapts while the fundamental property of constant width remains unchanged. The applet serves as an engaging bridge between abstract geometry and kinematic intuition, making it an excellent tool for exploring advanced topics in Euclidean geometry such as curves of constant width, rotational symmetry, and the elegant connections between polygons and curved figures.