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.
Shoshichi Kobayashi has written: 'Foundations of differential geometry' 'Transformation groups in differential geometry' -- subject(s): Differential Geometry, Geometry, Differential, Transformation groups
WilliamL Burke has written: 'Applied differential geometry' -- subject(s): Differential Geometry, Geometry, Differential
Journal of Differential Geometry was created in 1967.
Bansi Lal has written: 'Three dimensional differential geometry' -- subject(s): Differential Geometry, Geometry, Differential
Dirk J. Struik has written: 'Lectures on classical differential geometry' -- subject(s): Differential Geometry, Geometry, Differential
M. Francaviglia has written: 'Applications of infinite-dimensional differential geometry to general relativity' -- subject(s): Differential Geometry, Function spaces, General relativity (Physics) 'Elements of differential and Riemannian geometry' -- subject(s): Differential Geometry, Riemannian Geometry
Otto Haupt has written: 'Geometrische Ordnungen' -- subject(s): Algebraic Geometry, Differential Geometry, Geometry, Algebraic, Geometry, Differential
Gillian Margaret Brown has written: 'Metric differential geometry' -- subject(s): Calculus of tensors, Differential Geometry, Generalized spaces, Geometry, Differential
Patrick Eberlein has written: 'Geometry of nonpositively curved manifolds' -- subject(s): Differential Geometry, Geometry, Differential, Manifolds (Mathematics) 'Geodesics and ends in certain surfaces without conjugate points' -- subject(s): Differential Geometry, Geodesics (Mathematics), Geometry, Differential, Manifolds (Mathematics), Riemann surfaces
Luther Pfahler Eisenhart has written: 'Non-Riemannian Geometry (Colloquium Publications (Amer Mathematical Soc))' 'Non-Riemannian geometry' -- subject(s): Differential Geometry, Geometry, Differential 'Riemannian geometry, by Luther Pfahler Eisenhart' -- subject(s): Differential Geometry, Geometry, Differential, Riemann surfaces 'Transformations of surfaces' -- subject(s): Surfaces, Transformations (Mathematics)
Ernest Julius Wilczynski has written: 'Projective differential geometry of curves and ruled surfaces' -- subject(s): Projective differential geometry, Differential Geometry, Surfaces, Curves
Wilhelm Blaschke has written: 'Gesammelte Werke' -- subject(s): Geometry, Mathematics 'Nicht-euklidische Geometrie und Mechanik I, II, III' -- subject(s): Mechanics, Geometry, Non-Euclidean 'Kreis und Kugel' -- subject(s): Differential Geometry, Geometry, Differential 'Ebene Kinematik' -- subject(s): Kinematic geometry 'Elementare Differentialgeometrie' -- subject(s): Differential Geometry, Geometry, Differential