Graph of the function y = f(t), t being the rotation angle of a rectangle about its gravity center and y being the area of the enclosing frame E1...E4. y obtains its maximum value when the enclosing is a square. The minimum of y occurs at multiples of π/2. How to explain that at the maximums we have tangents whereas at minimums we have only left/right tangents?
C controls the rotation angle. Switch to the "Select on contour" tool (press CTRL+2), catch and move C, to see the variation of the area (point X on the graph of function f(t)).
![[alogo]](alogo.png){kind=small}
Enclosing rectangle of rotated rectangle ![[0_0]](EnclosingRotated_files/EnclosingRotated_0_0_0.png)
![[0_1]](EnclosingRotated_files/EnclosingRotated_0_0_1.png)
![[0_2]](EnclosingRotated_files/EnclosingRotated_0_0_2.png)
![[1_0]](EnclosingRotated_files/EnclosingRotated_0_1_0.png)
![[1_1]](EnclosingRotated_files/EnclosingRotated_0_1_1.png)
![[1_2]](EnclosingRotated_files/EnclosingRotated_0_1_2.png)