Introduction
Curves in Motion: Algebraic and Conic Geometry with GeoGebra
Welcome to Algebraic Curves and Conics
Have you ever wondered how a simple equation can draw a beautiful shape? From the perfect roundness of a circle to the sweeping curves of a parabola or the twisting loops of more advanced curves, algebraic equations bring geometry to life.
In this book, you’ll explore algebraic curves—the set of points that make an equation true. We’ll start with familiar shapes called conic sections (circles, ellipses, parabolas, and hyperbolas) and then move into more exciting territory, where curves can loop, cross themselves, or even create striking patterns.
Using GeoGebra, you won’t just read about these curves—you’ll see them come alive. You’ll be able to:
- Play with equations using sliders to see how curves change.
- Discover how simple rules can create surprisingly complex designs.
- Connect algebra to real-world ideas like orbits, reflections, and engineering.