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Differential Geometry

Differential geometry is a field of mathematics which possesses similarities to the study of calculus, but differs in how it applies the techniques of integration and differentiation to more complex, higher dimension problems. Differential geometry can study any geometric shape from standard figures to more complex ones, but primarily studies dimensional manifolds. Additionally, curved planes are an area of focus in differential geometry.

Uncovering the geometry of space and time is a major application of this mathematical field. For example, general relativity, a theory developed by Albert Einstein, used the concepts of differential geometry to define space and time in terms of the shape they take on, which led to the formation of the concept of gravity.

Considering that differential geometry allows the user to understand the curvature of space and time, this allows it to be applicable and useful in all types of fields. For instance, geological structures can be described through the techniques of differential geometry, similar to how shapes can be analyzed for computer vision using differential geometry.

The aspects of geometry, specifically narrowed in on the concept of curvature are at the heart of differential geometry. Although differential geometry is a rather abstract field of study which requires the ability to visualize shapes and curves, it has many applications for today’s society. 

Proofs of the Fibonacci Sequence

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