What is a Perfect Ellipse and does it really exist?

Question

I am told that the "Ellipse" is the shape which has not been yet found to be "Perfect Shape" like "SQUARES,CIRCLES etc which are perfect shapes"-Why is the ellipse not a perfect shape?And if it is a perfect shape where is the proof of existent of such a perfect ellipse?Some say that "Shiv-Linga"-phallic symbol of Lord Shiva and the relegious Hindu icon has the shape of a perfect ellipse-is that true?

Answer 1

I guess you could say that squares and circles are perfect while ellipses are not because all squares are similar, that is, proprotional, to one another, and all circles are similar or proportional to one another, while all ellipses are not. The reason for this is that squares and circles are defined by their internal proportions. that is, a square is a quadrilateral whose all sides are equal or congruent, and whose all angles are equal or congruent. A circle, likewise, is the set of all points on a plane which are equidistant from a center point. You need very little information to define a circle or a square.

An ellipse is the set of all points which are a constant sum of the distance from two foci. Here you need a lot more information to define an ellipse, The foci can be any finite distance apart; the constant sum can take any finite value, and the resultant ratio of the major and minor axes can also take on any finite value. If any of these values become infinite you have a parabola. It is not true that any ellipse is similar to any other ellipse.

In the context of a Shiva Linga, you could say that it is a perfect ellipse because its physical dimensions conform exactly to the mathematical description of an ellipse, without any bumps or deviations. It is very rare for any physical object to be perfect in this sense, because the physical world is full of bumps and deviations. In the same way, the elliptical orbits of planets are probably perfect ellipses, because the bumps and deviations would be caused by friction and other irregularities in the environment, of which there is very little in deep space.

Answer 2

The ellipse is a more general form than the circle. It's excentricity is anything below 1, and the circle has excentricity 0. So a perfect ellipse could be with a special excentricity such as the inverse of the golden mean. Why not? Or it could be that the ratio of the axes is the golden mean, which would give a different, slimmer shape.