Norman Window: Modifiable Explorer

A Norman window is a window that consists of a rectangle mounted by a semicircle. You can fix the perimeter of this Norman window using the input box at the bottom. For any given fixed perimeter, how can we determine the dimensions of such a window that maximizes the amount of sunlight that can pass through it?

Drag the LARGE POINT (bottom left) along the xAxis to create various Norman windows with fixed perimeter. What do you notice?