Solving Problems in Point Geometry: Insights and Strategies for Mathematical Olympiad and Competitions

For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of auxiliary graphics and cumbersome calculations. Inspired by Leibniz's query, this book introduces a groundbreaking method: point geometry. By operating directly on points, it integrates the strengths of coordinate, vector, and mass point methods, simplifying operations and problem-solving. Central to this method is the identity approach, which streamlines complex problems into concise equations, unlocking multiple propositions with ease. Through meticulously crafted examples, readers are invited to explore the joy of mathematical thinking. Beyond mathematics, point geometry holds promise for artificial intelligence, offering a simple yet rich knowledge representation and reasoning method. With most solutions generated by computer programs, the potential for simplifying reasoning methods is immense, paving the way for a brighter future in both education and AI advancement. In this ambitious endeavor, the authors seek to simplify knowledge representation and reasoning, reduce the burden of learning, and accelerate the progress of artificial intelligence. This book is not just a guide to geometry; it's a catalyst for transformative thinking and discovery.

Jingzhong Zhang, the academician of the Chinese Academy of Sciences, is currently a professor in Guangzhou University. He is a famous Chinese mathematician and computer expert, serves as the chairman of the International Association for Educational Mathematics, and was the chairman of the China Science Writers Association. He is mainly engaged in the research of mechanical theorem proving in geometry, educational information technology, educational mathematics, and is devoted to the creation of popular science in mathematics. He has proposed a new Geometric Algebra, Point Geometry. He has received seven important national awards, including the State Natural Science Award of China, the State Science and Technology Advancement Award of China, and the National Teaching Achievement Award of China.

Xicheng Peng, who works at Central China Normal University, is passionate about popularizing mathematics through written discourse. He has authored over ten works in popular science in mathematics. In recent years, he has been engaged in the research of mechanical theorem proving in Point Geometry and educational mathematics, proposed algorithms for point geometry identity equations and complex geometry identity equations.