Videos, and Games
||Prof. Dr. Ulrich Pinkall
- [27.01.06] Check out this survey article on Octonions.
- [03.01.06] I have posted a solution to the exercise from Assignment 8 regarding the axis of a linear complex.
- [26.12.05] Charles Gunn will not have office hours on January 2. Instead, he will offer office hours on January 4, 2:00-3:00 pm, in MA 319 as usual.
- [21.12.05] There is now a short document dealing with isometries of the hyperbolic plane with some worked out examples.
- [15.12.05] There is a short document describing the matrix form for a null system and its inverse (dual).
- [02.11.05] Regarding the final test (Klausur): students should be prepared to pass a verbal (muendlich) test at the end of the course. The teaching staff will decide on an individual basis if a student is required to pass such a test.
- [28.10.05] Small typo in Hausaufgabe 1.ii): There is a missing ''with'' in the first sentence. The correct phrase is " ...such that there exists a line segment joining P and Q with no point in common with ..."
- [28.10.05] There is a guide to notation used in this course for download in case you weren't present at the practice session.
- [21.10.05] There is a correction to Exercise 4-i) from the first assignment sheet.
- [20.10.05] The Uebung will take place on Friday, 12-14, in MA-313. The first assignment is also due at that time (not on Thursday as originally printed on the assignment sheet).
- Projective Geometry is one of the foundation disciplines of modern mathematics. In this course we will aim to acquire a basic understanding of its content, from a variety of perspectives. After this introduction, we will proceed to study how euclidean and non-euclidean geometry can be derived as specializations of projective geometry -- using the theory of quadradic forms from linear algebra. Finally, we'll turn to other related topics such as Moebius geometry, which studies geometric properties left unchanged by inversions in spheres.
- Wichtige Hinweis: Sie brauchen eine Lineal, Geo-dreieck, und eine harte Bleistift fuer die Uebung.
Theorem of Desargues
Projective Generation of a Point-wise Conic
The Punctured Torus Explorer allows the user to explore some discrete subgroups of PSL(2,C) corresponding to once-punctured tori.
- There are some related books on reserve in the mathematics library under the label GeometrieI (the books under Pinkall are for another course!).
- Coxeter, The Real Projective Plane. A classic text, which develops real projective geometry in the plane from first principles.
- Coxeter, Non-euclidean Geometry. A classic text, in which non-euclidean geometry is developed from first principles out of projective geometry.
- Dorwart, The Geometry of Incidence. A simplified introduction to the basic concepts of projective geometry.
- Samuel, Projective Geometry. A modern, abstract approach.
- Pedoe, An Introduction to Projective Geometry. More geometric approach; first chapter has good examples.
- Beutelspacher, Projektive Geometrie. A modern approach, with lots of examples and some new applications to structural analysis and cryptology.
- A pdf file containing the soon-to-be-published book Projektive and Cayley-Kleinsche Geometrien by A. L. Onishchik and R. Sulanke. This is available for use by students in this course only.
- A related script by Nigel Hitchin, University of Texas.
- A survey article on octonions by John Baez, University of California, Riverside.
- Zirkel, dynamic geometry software by R. Grohlmann.
- Successful completion of the course will be determined by completion of 50% of the homework problems, participation in the practice sessions, and (possibly) passing a final verbal test (muendliche Klausur). The test will be given on an individual basis as determined by the professor and assistant.
- New material needed for the exercises may be introduced in the practice sessions. Please speak with the assistant if you have problems with attending.
- In principle, working in groups is encouraged. However, the write-up of the homework problems is to be completed by each student individually.
- The assistant is American and may use English when writing; however, he will try to speak German as much as you can bear.
- Problem sheets will be handed out at the Uebungen; they are also available at the same time on this web page above.
- Due dates for homework assignments are sharp: no extensions will be given without a medical excuse.
- Depending on the time available for correction, it may be that not all problems are corrected each week, but rather a random sub-sample of the homework problems are chosen to be corrected. The solutions for ALL problems will in any case be posted on the web-site below. Only those problems which are corrected will be included in calculating the 50% limit required for receiving a certificate.