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.axioms propositions  how these propositions could be fit into a comprehensive deductive and logical system. [2]logical system [2]

Truthiness  true in an absolute sense.  self-consistent non-Euclidean geometries self-consistentnon-Euclidean geometries

Non-Euclidean Geometry ?  study of shapes and constructions  hyperbolic and elliptic geometry hyperbolicelliptic geometry  The essential difference

 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.  euclidean and non-euclidean geometry were coordinated, and each of them subordinated to new types of geometry. The classical postulational treatments obtained different results.