Rational Curves

Rational curves are geometric shapes defined by equations that can be expressed using simple ratios of polynomial functions, similar to how fractions work. Imagine a curve on a surface that can be described entirely by algebraic formulas with ratios of straightforward polynomials; these are rational curves. They are important in mathematics because they serve as the building blocks for understanding more complex shapes and have applications in areas like computer graphics and algebraic geometry. Essentially, rational curves represent the simplest type of algebraic curves, characterized by their describability through rational functions.