A space curve is a curve that exists in three-dimensional space, which means it can be described using a vector function that takes a real parameter and maps it to points in $ ext{R}^3$. Unlike curves confined to a plane, space curves can twist and turn in any direction, allowing for a rich variety of shapes and behaviors. The study of space curves involves understanding their parametrization and their properties such as curvature and torsion, which provide insights into their geometric nature.
congrats on reading the definition of space curve. now let's actually learn it.