What is the minimum eccentricity an ellipse can have

Zero (the ellipse is a circle)

Explanation:

The eccentricity of an ellipse is defined as the ratio between the distance of each focus from the centre of the ellipse (c) and the length of the semimajor axis (a):

For a perfect circle, the focii correspond to the centre of the circle, so

c = 0

which means that for a circle,

e = 0

Therefore, the minimum value of the eccentricity of an ellipse is zero, and it occurs when the ellipse coincides with a circle.

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