In everyday life an ellipse is recognized as an orthogonal projection of a circle to a plane. The history of mathematics tells us, that the ellipse as a conic section was already studied by Apollonius of Perge in the third and second century BC. Only after more than a thousand years, Johannes Kepler and Isaac Newton discovered its applicability, namely to describe the planetary motion around the Sun. Certain distinctive property of ellipse also allows us to help in constructing the Cassini curves. By using Binet´s equation we also deal with the motion of a particle around a fixed attracting center. With the mathematical methods we solved problems also in geometrical optics. By using Fermat's principle in optics and calculus of variations we find the path of light rays in Eaton lens. We will also show, how the computer endowed by a suitable software, such as GeoGebra, help us discover properties of Eaton lenses.
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