It is a field of math that uses calculus, specifically, differential calc, to study geometry. Some of the commonly studied topics in differential geometry are the study of curves and surfaces in 3d
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Analytical geometry is used widely in engineering. It set the foundation for algebraic, differential, discrete, and computational geometry. It is the study of geometry using a coordinate system.
Mathematicians study various types of geometry, but the most common ones include Euclidean geometry, which studies flat, two-dimensional space, and three-dimensional space; and non-Euclidean geometry, which explores curved spaces such as spherical and hyperbolic geometries. Differential geometry is another branch that focuses on the study of curves and surfaces using calculus techniques, while algebraic geometry investigates geometric objects defined by algebraic equations. Finally, fractal geometry delves into the study of intricate, self-repeating geometric patterns.
These are the general math courses in an undergraduate program of Mechanical Engineering. Actually, these are also the math courses required in ANY undergraduate Engineering curriculum: Algebra Trigonometry Analytic Geometry Differential Calculus Integral Calculus Mutivariable Calculus Differential Equations
As an automotive engineer, I mostly use algebra, but I sometimes use geometry, statistics, and calculus. Some higher level research positions may use differential equations.
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.