Geometry revealed

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Both classical and modern differential geometry have been vital areas of research throughout the 20th century, central to many advancements in mathematics and physics. This book aims to cultivate a modern geometric culture through a series of visually appealing unsolved or recently solved problems that necessitate the development of concepts and tools of varying abstraction. It begins with fundamental objects such as lines, planes, circles, spheres, polygons, polyhedra, curves, and surfaces, elucidating crucial ideas and abstract concepts essential for achieving results. These concepts build progressively, akin to Jacob's ladder, allowing for increased abstraction. The book illustrates the enduring spirit of geometry, emphasizing that even "elementary" geometry remains vibrant and integral to the work of contemporary mathematicians. It highlights the countless unexplored paths and concepts waiting to be discovered. Rich in visual content, the book invites readers to engage with it at random, offering enjoyment based on their own intuitions and interests. Authored by Marcel Berger, a prolific writer on geometry, this work is designed for students and teachers of mathematics who have a passion for the subject.