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On an experimental topology

Topology is the mathematical study of properties of objects which are preserved through deformations, twisting, and stretching. Tearing, however, is not allowed. A square is topologically equivalent to a circle and a circle is topologically equivalent to an ellipse, into which it can be deformed by stretching. In this work, we discuss the properties of ellipses when an ellipse is continuously subjected to deformation by stretching.