Euclidean and Non Euclidean Geometries (MAE727)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Euclidean and Non Euclidean Geometries

Independent Teaching Activities

Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek, English

Is the Course Offered to Erasmus Students


Course Website (URL) 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.

General Competences
  • Working independently
  • Decision-making
  • Production of free, creative and inductive thinking
  • Criticism and self-criticism


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


Classroom (face-to-face)

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
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.