Traditional Culture Encyclopedia - Photography major - Do circles and ellipses with the same circumference also have the same area? Why?

Do circles and ellipses with the same circumference also have the same area? Why?

In high school, I remember learning the area photography theorem

The projection of an ellipse is a circle

Consider a cylinder and then cut it diagonally by a plane Now

The upper surface is an ellipse, and the lower surface (that is, the projection of the upper surface) is a circle

The radius of the circle is the minor axis of the ellipse b

cosA= b/a (Known by drawing)

According to the area projection theorem

S (ellipse) = S (circle)/cosA = PI*ab

The circle The area is directly the square of PAI*R