classical geometry euclidean transformational inversive and projective pdf cbsg

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==> classical geometry euclidean transformational inversive and projective pdf <==

Classical geometry encompasses several branches, including Euclidean, transformational, inversive, and projective geometry, each focusing on different properties and transformations of geometric figures. Euclidean geometry, founded by Euclid, deals with flat spaces and includes the study of points, lines, angles, and shapes based on axioms and theorems. Transformational geometry studies the properties of figures that remain invariant under various transformations, such as translations, rotations, reflections, and dilations. Inversive geometry focuses on properties that are preserved under inversion, typically in a circle, emphasizing the relationships between points and circles, and often revealing fascinating insights into congruence and similarity. Projective geometry, on the other hand, extends the concepts of geometry to include points at infinity, allowing for the study of properties invariant under projection. This branch explores the relationship between points and lines in a more abstract manner, eliminating the need for distance and angle measurements, which leads to a deeper understanding of geometric configurations. Together, these branches provide a comprehensive framework for understanding geometric relationships and transformations in various contexts.