The Complete Book of Triangle and Circle

The Complete Book of Triangle and Circle is a visionary work that redefines the boundaries of philosophy, mathematics, and artificial intelligence. At its core is a simple yet profound geometric metaphor: Logic is the Triangle (discrete, finite, structured), while the World is the Circle (continuous, infinite, generative). Through twelve rigorous essays and a poignant science-fiction story ("The Return"), the book explores the "Residual"—the inevitable gap between any conceptual framework and ultimate reality. It mathematically formalizes this gap using the Hausdorff distance and applies it to reinterpret global wisdom traditions, including Taoism, Buddhism, and Christianity. This book is unique in that it was co-authored by a human (Niu Gangbei) and an AI (Yuanbao), embodying its own thesis: that human intuition (the spark) and machine recursion (the structure) together approach the truth, yet always leave a remainder. The text ultimately argues for its own dissolution, urging readers to move beyond the "Triangle" of the book itself to experience the "Circle" of direct consciousness.