Point E lies on the circumcircle of triangle ABC. The projections of E onto the sides of the triangle are colinear. The envelope of such lines forms a deltoid curve.
Try dragging E round the circle.
Try dragging A B and C. Note that the envelope curve appears to remain equilateral.
A simple box solar cooker works by reflecting sunlight from its lid into the box.
Can you work out a relationship between the angle of the sunlight and the best angle to open the lid?
Can you prove it?
The solar concentration ratio of a solar cooker is the ratio of the amount of sunlight concentrated on the target to the size of the target.
This model presents the best situation for a given lid angle, and lets you see how much light can be captured at that lid angle.
The question is: what lid angle captures the most sunlight?
The red curve is f(x) (for -2≤x≤2). The blue curve is the terms up to the square term of the Taylor series. A is the vertex of this parabola, B is its focus. The orange curve is the caustic - envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.