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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.
No, algebra is not arithmetic. While both algebra and arithmetic involve numbers and mathematical operations, algebra is a branch of mathematics that goes beyond the basic arithmetic operations (addition, subtraction, multiplication, and division) to include variables, equations, and abstract mathematical concepts.
Geometry is a field of mathematics and is neither a science nor an occupation. Any other field of mathematics can be related to geometry. Trigonometry and algebra are among the most closely related. Occupations that use geometry include engineering, physics, and astronomy, but many others do as well.
Albert Einstein.
The man JOB in the Book of Job.