Handout # 3

Math 5392 Finite Geometries I Summer 2004

Dr. Cordero                                                                                  

Affine Planes

Additional Problems

1. Draw a Desargues configuration using a  elation.
2. Which of the axioms of an affine plane have valid duals in the affine plane?
3. Draw an affine plane with 16 points.
4. Show that there is no affine plane with 29 points.
5. Give the parallel classes in the affine plane of order 3.
6. Show that an affine plane always has an even number of lines.
7. Embed the affine plane of order 3 in the projective plane of order 3.
8. Find  non-identity  collineations of the affine plane of order 3 and 4.
9. Show that the affine plane of order 2 is unique.
10. Show that any affine plane satisfies axiom 3 of projective planes (There exists 4 points no three of which are collinear.).
11. Show that the affine plane of order 2 has no non-identity homothety.
12. Find a non-identity homothety of the affine plane of order 3.
13. Find an example of a non-identity affine perspectivity in the affine plane of order 4.
14. Find a Desargues configuration in the affine plane of order 3.