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Dive into the world of Non-Euclidean Geometry and understand its concepts, including hyperbolic and elliptic geometry. Discover the differences with Euclidean Geometry and how new systems are based on Euclid's principles.
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Non-Euclidian Geometry Maryam Amini
Main Objectives: • Understand the basic idea of Euclidean Geometry • Understand the basic idea of non-Euclidean Geometry • Conclusion
What is Euclidean Geometry? • is a mathematical system • assuming a small set of intuitively appealing axioms, and deducing propositions. • how these propositions could be fit into a comprehensive deductive and logical system.[2]
Truthiness • true in an absolute sense. • self-consistentnon-Euclidean geometries
Non-Euclidean Geometry ? • study of shapes and constructions • hyperbolic and elliptic geometry • The essential difference
Concepts of Non-Euclidean Geometry • Basing new systems on the Euclid’s systems • are any forms of geometry that contain a postulate (axiom) which is equivalent to the negation of the Euclidean parallel postulate.
Conclusion: • euclidean and non-euclidean geometry were coordinated, and each of them subordinated to new types of geometry. The classical postulational treatments obtained different results.
