A golden ellipse is one where the axes are in golden proportion, meaning the ratio of the major axis (a) to the minor axis (b) is the golden ratio:
φ = (1 + √5)/2.
To visualize this, draw a golden ellipse along with its inscribed and circumscribed circles: the smallest circle fitting inside the ellipse and the largest circle surrounding it.
Interestingly, the area of the ellipse matches the area of the “annulus” formed between these two circles!
Here’s how it works:
Let a be the semi-major axis and b the semi-minor axis, with a = φb.
The area of the annulus is:
π(a² − b²) = πb²(φ² − 1)
The area of the ellipse is:
πab = πφb²
And as φ² − 1 = φ, then πb²(φ² − 1) = πφb².
Isn’t it fascinating how geometry intertwines with the golden ratio?
