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In general relativity, a world line is a curve in spacetime.If Algebraic curves are the curves considered in algebraic geometry.
For example, in Book I of Euclid's Elements, a line is defined as a "breadthless length" (Def.
The image of simple plane curve can have Hausdorff dimension bigger than one (see Koch snowflake) and even positive Lebesgue measure (the last example can be obtained by small variation of the Peano curve construction). Roughly speaking a differentiable curve is a curve that is defined as being locally the image of an injective differentiable function While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions.
The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions.
In the eighteenth century came the beginnings of the theory of plane algebraic curves, in general.
Newton had studied the cubic curves, in the general description of the real points into 'ovals'.