Definition: Contractibility is a concept in mathematics that refers to whether two mathematical objects are equivalent or interchangeable. In other words, if one object can be transformed into another without changing its properties, then they are said to have contractibility. For example, consider the equation x^2 + y^2 = 1. This equation represents a circle with center at (0, 0) and radius 1. If we were to transform this circle by rotating it 90 degrees clockwise or 9