Line Geometry
| Title | ΕΥΘΕΙΑΚΗ ΓΕΩΜΕΤΡΙΑ / Line Geometry |
| Code | 0666 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Stylianos Stamatakis |
| Common | No |
| Status | Active |
| Course ID | 40002461 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 9
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A3 | 1 | 1 | 10 |
| THEŌRĪTIKĪ PLĪROFORIKĪ KAI THEŌRIA SYSTĪMATŌN KAI ELEGCΗOU | Elective Courses | 1 | 1 | 10 |
| Academic Year | 2020 – 2021 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600177925
|
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600177925
- Other: http://stamata.webpages.auth.gr/geometry/
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
- French (Examination)
- German (Examination)
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
Course Content (Syllabus)
A. Introduction: Cayley-Klein geometies and the Erlangen-Program of Felix Klein. The n-dimensional affine space. and the n-dimensional projectiv space.
B. Ruled surfaces: Conical, cylindrical and tangential ruled surfaces. The right helicoid, ruled surfaces of Ch. E. Catalan. Conoidal ruled surfaces. Developability condition and developable ruled suρfaces. The parameter of distribution and the striction line. The moving frame of E. Kruppa. Derivative equations of G. Sannia. Complete system of invariants. Envelope of an 1-parameter family of planes. Accompanying developable ruled surfaces. Ruled surfaces of constant slope. Ruled surfaces of constant parameter of distribution. Closed ruled surfaces. Linear span.
C. Plücker's line coordinates of a straight line in P^3. The hypersurface of the second order of Plücker and the Plücker-Klein mapping. Straight lines and 2-dimensional generators of the Plücker hypersurface. Linear complexes of straight lines. Polarity systems. Linear congruences of straight lines.
Keywords
Ruled surfaces, line geometry, Plücker's line coordinates
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 125 | 4.2 | ✓ | ✓ | |
| Reading Assigment | 10 | 0.3 | ✓ | ✓ | ✓ |
| Tutorial | 32 | 1.1 | ✓ | ✓ | ✓ |
| Written assigments | 10 | 0.3 | ✓ | ✓ | |
| Exams | 3 | 0.1 | ✓ | ✓ | |
| Total | 180 | 6 |
Student Assessment
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
- S. P. Finikow: Theorie der Kongruenzen. Berlin 1959
- V. Hlavaty: Diferentielle LinienGeometrie. Groningen 1945
- J. Hoschek: Liniengeometrie. Zürich 1971
- H. Pottmann, J. Wallner: Computational Line Geometry, New York 2001
- R. Sauer: Projektive Liniengeometrie. Berlin und Leipzig 1937
- A. Svec: Projective differential geometry of line conruences. Prag 1965
- E. A. Weiss: Einführung in die Liniengeometrie und Kinematik. Leipzig und Berlin 1935
- E. J. Wilczynski: Projective differential Geometry of curves and surfaces. New York 1962
- Ν. Κ. Στεφανίδη: Διαφορική Γεωμετρία, Β’ έκδοση βελτ. και επαυξ. Θεσσαλονίκη, 2014
Last Update
27-05-2019
