Where algebra meets geometry. Explore the beautiful world of algebraic curves and discover the deep connections between polynomial equations and geometric shapes through 25 interactive demonstrations.
From simple lines to exotic curves, from conic sections to intersection theory — see how polynomial equations create stunning geometric objects.
Discover what algebraic curves are: the zero sets of polynomial equations. Explore lines, conics, and beautiful higher-degree curves.
Master the degree-2 curves: circles, ellipses, parabolas, and hyperbolas. See how they all arise from slicing a cone.
Learn the fundamental intersection theorem: two curves of degrees m and n meet in exactly m×n points (counted properly).
Explore cubic curves and the remarkable elliptic curves. Discover the group law that makes them central to modern cryptography.
Discover the natural home of algebraic geometry where parallel lines meet and every pair of curves intersects the "right" number of times.
The algebra-geometry dictionary: polynomial ideals correspond to geometric varieties. Master the Nullstellensatz.
The computational engine of algebraic geometry. Learn to solve polynomial systems and compute with ideals.