A shape rotates and passes perfectly through a cut-out template. How would you model the timing and geometry using 2D trigonometry?
A mesmerising video shows a 3D shape rotating and passing cleanly through a 2D template — but how? The key insight is timing: the rotating shape's cross-section changes continuously, and at exactly the right moment its profile matches the template. This exploration challenges students to model rotating shapes using 2D trigonometry and parametric equations. By expressing the shape's profile as a function of the rotation angle, students can determine when (and whether) it aligns with a given template. The mathematics connects circular motion, trigonometric functions, and the idea that a 3D object's 2D shadow depends entirely on the angle of projection.