Euclidean and Non Euclidean Geometry

Course Description

Axiomatic approach to Euclidean geometry. Use of logic in mathematical reasoning. Hilbert’s formulation. Removal of the parallel axiom. The discovery of non-Euclidean geometry. Hyperbolic geometry

Course Objectives & Outcomes
The objectives of this course are to:

• Use deductive method and logic to justify each step in the proof.
•  Distinguish between Euclid axioms and Hilbert axioms.
•  Distinguish between theorems of geometry without using parallel axiom and Euclidean geometry.
•  Know the Hyperbolic geometry.
•  Prove some Hyperbolic theorems in geometry 

On successful completion of this course students will be able to:

•  The student Uses deductiveaximes and logic to justify each step in the proof.
•  The student distinguishs between Euclid axioms and Hilbert axioms.
• The student distinguishs between theorems of geometry without using parallel axiom and Euclidean geometry.
•  The student must Know the Hyperbolic geometry.
•  The student must prove some .Hyperbolic theorems in geometry.

References

1. Marvin Jay Greenberg; (2007) , Euclidean & Non-Euclidean Geometry, Development and History, 4rd Edition, ISBN-13:978-0716799481, ISBN-10: 0716799480.
2. Robin Hartshorne ; (, 2000), Geometry : Euclid and beyond, Springer, ISBN-13:978-1441931450, ISBN-10: 1441931457.
3. D. Hilbert; (1977), Foundations of Geometry, Court Publishing Company, ISBN-13:978-0875481647, ISBN-10: 0875481647.
4.  D.W. Henderson and DainaTaiamina; (November 3, 2000), “Experiencing Geometry: In Euclidean, Spherical and Hyperbolic Spaces” , Prentice Hall, ISBN-13:978-0131437487, ISBN-10: 0131437488.

Course ID: MATH 451