Algebraic Curves

Algebraic curves are mathematical shapes defined by polynomial equations in two dimensions. They can be visualized as the set of points that satisfy an equation, like a simple line or a more complex shape like an oval or a loop. These curves can describe a variety of natural phenomena and are essential in fields such as geometry and computer graphics. They can be classified based on their properties, such as being smooth or having singular points. Algebraic curves bridge algebra and geometry, helping to explore relationships between numbers and shapes.