A plane curve is a two-dimensional curve that lies entirely on a flat plane. A synonym for this term could be a planar curve, which refers to any curve that exists within a flat surface or plane. Another term that is commonly used is a two-dimensional curve, which refers to any curve that is made up of only two dimensions - length and width. Other possible synonyms include flat curve, level curve, and unidimensional curve. Regardless of the terminology used, plane curves are important geometric objects that play a key role in mathematics, physics, and engineering, and understanding the different terms used to describe them is essential for those working in these fields.