# Euclidean and Non Euclidean Geometries (MAE727)

### General

School School of Science Department of Mathematics Undergraduate MAE727 7 Euclidean and Non Euclidean Geometries Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek, English Yes See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes This is an introductory course on non Euclidean geometries. The aim is to study how the attempt to prove Euclid's fifth postulate led the way to non Euclidean geometries. On completion of the course the student should be familiar with the foundations of Euclidean and non Euclidean geometries. Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

### Syllabus

Euclid's geometry, Hilbert's system of axioms, the fifth postulate, compatibility of axioms, neutral geometry, independence of the fifth postulate, hyperbolic geometry, Poincarẻ model, spherical geometry, Platonic solids.

### Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology -
Teaching Methods
Lectures (13X3) 39
Working independently 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

### Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

• Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
• M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
• R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
• H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.