Have you ever wondered if geometry could be more than just points, lines, and shapes? What if it wasn’t about measuring line segments and angles, but about understanding the directions you can look in and how different perspectives shape what you see? Projective geometry invites you to explore just that—to shift your viewpoint and see geometry as something much broader than what you’ve encountered before.

Consider those train tracks stretching into the distance. In ordinary geometry, parallel lines never meet, but your eyes see them converge at the horizon. Projective geometry takes this observation seriously, studying how lines behave as they extend toward, and even through infinity, and how objects relate to each other from different perspectives. It’s the mathematics behind the way artists create depth in their drawings or the way computer software builds 3D worlds out of 2D screens.

In this class, you won’t just sit and memorize formulas—you’ll explore the principles that connect geometry with art, technology, and the way we see the world around us. Along the way, you’ll discover how projective geometry offers a cleaner, more elegant theory with fewer exceptions to worry about. Our subject encourages a mindset of curiosity and discovery, showing that even the most abstract ideas reveal real connections to the spaces we interact with every day.