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[8] A plane curve is a curve for which X {\displaystyle X} is the Euclidean plane —these are the examples first encountered—or in some cases the projective plane . A space curve is a curve for which X {\displaystyle X} is at least three-dimensional; a skew curve is a space curve which lies in no plane.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.