Geometry

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This text is the fifth and final installment in a series of educational books by Israel Gelfand and his colleagues for high school students, focusing on foundational mathematics. Gelfand designed these materials for independent study, enabling students to learn at their own pace. This volume presents basic geometry differently than traditional methods; it emphasizes geometric constructions over formulae and logical deduction. Abundant illustrations and problems encourage readers to draw and manipulate figures, fostering their geometric vision, imagination, and creativity. The chapters are structured to introduce projective, affine, symplectic, and Euclidean geometries sequentially, ensuring students have the necessary tools for understanding. The book is suitable for a broad audience, including high school students, teachers, and anyone interested in enhancing their geometric intuition—skills valuable in various professions. Even experienced mathematicians can appreciate its unique approach to plane geometry, combining simplicity with depth and rigor. The text aims to provide an intuitive understanding of geometric concepts, making it accessible and engaging for all readers, regardless of prior knowledge.