A golden ellipse is an ellipse in which the aspect ratio of its two semi-axes and corresponds to the golden ratio.
Given is a annulus with outer radius and inner radius as well as an ellipse with semi-major axis and semi-minor axis , where and are positive real numbers.
Then the ratio corresponds to the golden ratio if and only if the annulus and the ellipse have the same area.
The proof results from the following equivalence chain:
Since only the positive solution is possible, after division by we get:
The golden ellipse can be inscribed in a golden rectangle with the side lengths and .