Mon Sept 13 Thomas Erlandsson, Introduction
Wed Sept 15 Lars Lindberg, Axioms of Incidence and Fields (Hartshorne Sec 6 and 14)
Mon Sept 20 Rodolfo Rios Z., Axioms of Betweenness and Ordered Fields (Hartshorne Sec 7 and 15)
Thu Sept 23 Jonathan Mörndal, Congruence of Segments and Angles (Hartshorne Sec 8, 9 and 16)
Mon Sept 27 Djalal Mirmohades, The Hilbert plane (Hartshorne Sec 10)
Thu Sept 30 Djalal Mirmohades, Circles in the Hilbert plane (Hartshorne Sec 11)
Thu Oct 14 Daniel Luna, Non-Archimedean Geometry Part I (Hartshorne Sec 18)
Mon Oct 25 Daniel Luna, Non-Archimedean Geometry Part II (Hartshorne Sec 18)
Thu Oct 28 Erik Andersson, The Area Problem (Hartshorne sec 22-24)
Mon Nov 1 Jonathan Mörndal, Quadratura Circuli (Hartshorne sec 25)
Wed Nov 3 Rodolfo Rios Z., Euclid's Theory of Volume and Hilbert's Third Problem (Hartshorne sec 26-27)
Mon Nov 8 David Larsson, The Regular 17-Sided Polygon (Hartshorne sec 29)
Mon Nov 15 Anders Södergren, On Mascheroni's Theorem
Thu Nov 18 David Larsson, The Regular 17-Sided Polygon, Part II (Hartshorne sec 29, 32)
Mon Nov 22 Erik Andersson, Rigid Motions and SAS (Hartshorne sec 17)
Mon Nov 29 Lars Lindberg, Licentiatseminarium
Tue Dec 7 Anders Södergren, On 3-dimensional Hyperbolic Spaces
Mon Febr 7 Oskar Westerstrand, On the Poincaré Model, Part 1 (Hartshorne sec 39)
Mon Febr 14 Oskar Westerstrand, On the Poincaré Model, Part 2 (Hartshorne sec 39)
Mon Febr 21, 10-12 am, Room 3513 Lars Lindberg, Hilbert's Arithmetic of Ends (Hartshorne sec 41)
| Ch. 1 | Euclid's Geometry |
| 1. | A First Look at Euclid's |
| 2. | Ruler and Compass Constructions |
| 3. | Euclid's Axiomatic Method |
| 4. | Construction of the Regular Pentagon |
| 5. | Some Newer results |
| Ch. 2 | Hilbert's Axioms |
| 6. | Axioms of Incidence |
| 7. | Axioms of Betweenness |
| 8. | Axioms of Congruence for Line Segments |
| 9. | Axioms of Congruence for Angles |
| 10. | Hilbert planes |
| 11. | Intersection of Lines and Circles |
| 12. | Euclidean planes |
| Ch. 3 | Geometry over Fields |
| 13. | The Real Cartesian Plane |
| 14. | Abstract Fields and Incidence |
| 15. | Ordered Fields and Betweenness |
| 16. | Congruence of Segments and Angles |
| 17. | Rigid Motions and SAS |
| 18. | Non-Archimedean Geometry |
| Ch. 4 | Segment Arithmetic |
| 19. | Addition and Multiplication of Line Segments |
| 20. | Similar Triangles |
| 21. | Introduction of Coordinates |
| Ch. 5 | Area |
| 22. | Area in Euclid's Geometry |
| 23. | Measure of Area Functions |
| 24. | Dissection |
| 25. | Quadratura Circuli |
| 26. | Euclid's Theory of Volume |
| 27. | Hilbert's Third Problem |
| Ch. 6 | Construction Problems and Field Extensions |
| 28. | Three Famous Problems |
| 29. | The Regular 17-sided Polygon |
| 30. | Construction with Compass and Marked Ruler |
| 31. | Qubic and Quartic Equations |
| 32. | Appendix: Finite Field Extensions |
| Ch. 7 | Non-Euclidean Geometry |
| 33. | History of the Parallel Postulate |
| 34. | Neutral Geometry |
| 35. | Archimedean Neutral Geometry |
| 36. | Non-Euclidean Area |
| 37. | Circular Inversion |
| 38. | Digression: Circles Determined by Three Conditions |
| 39. | The Poincaré Model |
| 40. | Hyperbolic Geometry |
| 41. | Hilbert's Arithmetic of Ends |
| 42. | Hyperbolic Trigonometry |
| 43. | Characterization of Hilbert Planes |
| Ch. 8 | Polyhedra |
| 44. | The Five Regular Solids |
| 45. | Euler's and Cauchy's Theorems |
| 46. | Semiregular and Face-Regular Polyhedra |
| 47. | Symmetry Groups of Polyhedra |
| Tillbaka till hemsidan | Tillbaka till kurser |