Code: 1-UDG-141/15

Continuous assessment: 2x written test Semester assignments. The submission deadline is by the end of the semester. Please send the completed assignments together in one email to my faculty email with the subject "ProjGeo:~Your name~". Any questions should also be directed there.

Final assessment: Examination consisting of a written and oral part

Exam tasks: assignment (9:50 16.6.2020)

Syllabus: 

1. Extended Euclidean plane and its properties. Projective plane. Duality.
2. Homogeneous coordinates. Desargues' theorem. 
3. Harmonic quadruples.
4. Projective mappings.
5. Collineations.
6. Pappus' theorem. The proof of theorem 6.2 is currently missing here, but it is already quite long as it is, so we will postpone it for later; meanwhile, I will add some examples. Solved example + gif.
7. Pappus' theorem II (continuation).
8. Cross ratio. This chapter will also be divided into several parts; exercises (apart from those in this text) will be added after completing the entire section.
9. Cross ratio II.
10. Equations of projectivities.
11. Equations of projective collineations.

Exercises: 

Exercises 4 

I recommend reading the commentary on the first example and then viewing this (gif). Subsequently, you can solve examples 2 and 3 by similar reasoning.

Solution to exercise 2 and animation.

Exercises 5 

Exercises 6

Exercises 7

Exercises 8

Exercises 9

Solutions and guides for exercises 4 and 5

Solutions and guides for exercises 6 and 7

Solutions and guides for exercises 8 and 9

 Images and sketches:

Representation of homogeneous coordinates of the extended Euclidean plane in three-dimensional space. Image and commentary.

Central projection of the "window" ABCD using Desargues' theorem. Image.

Uniqueness of the fourth harmonic point. Image.

Literature: