Modern Geometry: Axioms, Models, and Non-Euclidean Spaces

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Description: Explore the Geometry That Goes Beyond Triangles and Circles—Into the Logical Foundations of Space ItselfMost students encounter geometry as a set of rules for measuring angles, calculating areas, and proving theorems about triangles and circles. But Modern Geometry is something entirely different. It’s not just about shapes—it’s about the structure of space, the logic of axioms, and the mathematical systems that define how we understand the world.This course is a deep and intellectually rich journey into the axiomatic foundations of geometry, where we don’t just accept the rules—we question them, reconstruct them, and explore what happens when we change them. You’ll begin by learning the Axiomatic Method, the formal process by which entire mathematical worlds are built from a handful of assumptions. From there, you’ll explore models of geometry, including finite systems like Fano and Young geometries, and discover how different sets of axioms lead to radically different geometric realities.You’ll move beyond the familiar Euclidean framework into Incidence Geometry, Affine Geometry, and the vast landscape of Non-Euclidean Geometry—including Spherical, Hyperbolic, Projective, and Elliptic geometries. These aren’t just theoretical curiosities—they’re essential to understanding modern physics, computer graphics, and the very nature of space and time.Along the way, you’ll study the Betweenness Axioms, Ordered Geometry, and the logic behind congruence, angle relationships, and triangle theorems—not as static facts, but as consequences of deeper structural rules. You’ll see how parallel postulates shape entire geo
Category: Teaching & Academics > Other Teaching & Academics > Geometry
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Price: 39.99
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Source: Impact
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