Question

Here's one that should swift and easy for someone with a sense of geometry. The matter is very urgent, if I may say. Imagine two squares on plane F, initially sharing the same 4 points as corners. Square number 2 starts rotating on the plane F; changing its angular displacement but still sharing the same center point with square 1. Now, let's plot angle z on the x-axis and the shared area of the two squares on the y-axis. Is the graph sinusoidal?

Answer 1

The overlap in area of the two squares (of unit area) is given by
\[ \frac{ \tan\left(\frac{x}{2}+1\right)}{\sin(x)+1 }\]
valid for 1/4 turn, \(0≤ x ≤ \frac{\pi}{2} \)

Answer 2

that is fantastic, already, but could you demonstrate this on a diagram, perhaps? i might be able to try understand this without further explanation, but i am too busy to do that right now, mid term exam week