Geometry Revealed

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Both classical and modern differential geometry have been pivotal in 20th-century research, significantly influencing recent advancements in mathematics and physics. This book aims to cultivate a modern geometric culture through a series of visually engaging unsolved or recently solved problems that necessitate the development of various abstract concepts and tools. It begins with fundamental geometric objects—lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, and convex sets—while elucidating crucial ideas and abstract concepts essential for achieving results. These concepts build upon one another, akin to Jacob's ladder, allowing for increasing abstraction. The book highlights the enduring vitality of geometry, demonstrating that even "elementary" geometry remains central to the work of contemporary mathematicians. It emphasizes the vast array of unexplored paths and concepts waiting to be discovered. Richly illustrated and inviting, the book encourages readers to explore at their own pace, finding enjoyment in their individual intuitions and interests. Authored by Marcel Berger, known for his successful works on geometry, this book is designed for students and teachers of mathematics who have a passion for the subject.