If b/a is the ratio of semi-major to semi-minor axis then we can calculate its eccentricity using the formula
The eccentricity is a positive number less than 1, or 0 in the case of a circle. The greater the eccentricity is, the larger the ratio of a to b, and therefore the more elongated is the ellipse. Moreover, the distance between the foci is 2ae.
A paradox is an argument that starts with apparently acceptable assumptions and leads by apparently valid deductions to an apparent contradiction. Since logic admits no contradictions, either the apparently acceptable assumptions are not acceptable, or the apparently valid
deductions are not valid, or the apparent contradiction is not a contradiction. A paradox moves us to reexamine the argument until we find out what is wrong.
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