Some Courses in Geometry at the University of Technologie in Graz Sybille Mick

1. Some Courses in Geometry at the University of Technologie in Graz Sybille Mick Meeting of the Croatian Society for Geometry and Graphics in Zagreb February 24, 2007

2. SUPPLEMENTARY COURSES DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING GEOMETRY FOR MACHANICAL ENGINEERING

4. A supplementary examination about Descriptive Geometry is required if first-year students have a high school diploma (Matura) without Descriptive Geometry. The courses are a service at the university to train the students to take the supplementary examination in Descriptive Geometry.

6. STUDENTS First-year students with a high school diploma (Matura) without Descriptive Geometry BACKGROUND OF EXPERIENCE Knowledge from mathematics at secondary school

7. ADDITIONAL INFORMATION Semester hours 2 + 2 (a total of 60 teaching units) ME, ME-E: Intensive course at the end of the long vacation (2 weeks) A, CE: Intensive course at the beginning of thewinter semester (5 weeks)

8. STUDENTS Students in a preparatory course (second-chance education) BACKGROUND OF EXPERIENCE Knowledge from professional practice as draftsman, carpenter, plumber, ...

9. ADDITIONAL INFORMATION Semester hours 3 + 3 (a total of 90 teaching units) Course during the winter semester

10. New curriculum in secondary schools • New curricula in: Mechanical Engineering Mechanical Engineering - Economics Architecture Civil Engineering • New curriculum in our supplementary courses

11. Projections • Mathematical Resouces • Special Surfaces • CAD

12. Axonometric Projection • Piercing Points • Intersection of Planes • Intersection of Prisms and Pyramids • Orthographic Projection • Principal and Auxiliary Views • Perpendicularity • Construction of Distances • Construction of Angles • Orthographic Projection of Circles and a Conics

13. Objects • Tools • Transformations • 2D and 3D Constructions • Geometric Modeling (i.e. Boolean Operations) • Use of Auxiliary Coordinate-Systems

14. Coordinate-Systems • Objects (Polygons, Circles, Conics) • Objects (Prisms, Platonic Polyhedra, Pyramids) • Transformations

15. Examination 4 tasks • 1. Intersection of prisms in axonometric view or • Construction of a polyhedra in the three principal views (8 points) • 2. Surface (sphere, cylinder or cone of revolution) with plane intersections in the three principal views (8 points) • 3. Construction of an axonometric view of an object given in the three principal views (4 point) • 4. Question about CAD – progams (4 points)

16. Exam November 2006 • Cube • Plane sections of a cone • Axonometric view of an object • Theoretical question about CAD-Packages

18. Exam January 2007 • Intersection of prisms • Shere and cylinder of revolution • Axonometric view of an object • Theoretical question about CAD- . Packages

21. Training of spatial imagination by the help of geometric knowledge • Reaching sufficient constructive and analytic expertise in dealing with geometric objects and projection methods

22. WEEKLY HOURS: Lecture and Laboratory : 4 hours STUDENTS: First-year studentsBACKGROUND OF EXPERIENCE:Knowledge from education at secondary school or a supplementary course in Descriptive Geometry

23. SKRIPT ONLINE DOCUMENTS AND MANUALS OTHER EQUIPMENT: Graphical Instruments

24. Topographic Projection (10 + 10 hrs) • Surfaces ( 12 + 6 hrs) • Intersection of surfaces (4 + 10 hrs) • Perspective Projection (4 + 4 hrs)

25. Manfred SPITZER:Lernen (2002). Concept of a lesson (H. J. Wresnik, S. Mick) Students work on their own (30 min): Students work with instruction (60 min):

26. Lesson: RAILWAY UNDERPASS Students work on their own (30 min): Training of termsFill-in text THEORETICAL KNOWLEDGEMultiple choice Construction GRAPHICAL SKILLS(or Computation)

31. Lesson: RAILWAY UNDERPASS Students work with instructions (60 min): Materials: Description of the taskSheet to construct it on Hints to the solutionResult

38. INTERSECTION OF SURFACES – CONSTRUCTION AND COMPUTATION

39. PERSPECTIVE PROJECTION

40. Obligatory attendence and Satisfactory performance in two tests and a final written examination

42. Ideas for the solution to technical problems are important. To recognize the geometrical part of a problem is a first step. One of the main objectives of the lecture for engineers is to establish this geometric background.

43. WEEKLY HOURS: Lecture: 2 hours Laboratory: 1 hour Tutorial: 1 hour (voluntary)STUDENTS: Second-year studentsSTUDENTS´ PREREQUISITES:Knowledge from education at secundary school or a supplementary course in Descriptive Geometry

44. SKRIPT ONLINE-ADVISES SOFTWARE: Maple, ProE OTHER EQUIPEMENT: Graphical Instruments

45. Mathematical foundation • Curves and surfaces • Intersection of surfaces

46. tP Kurventangente k Krümmungskreis P M Hauptnormale Krümmungsmitte Figur 10: Der Krümmungskreis oskuliert die Raumkurve im Punkt P. • Mathematical foundation (8 hrs) • Displacements 2D and 3D • Curves and Surfaces

47. Pro/Engineer • Surfaces (16 hrs) • Algebraic Surfaces (e.g. Surfaces of second order) • Cylinders and Cones • Surfaces of Revolution

48. DEVELOPABLE NOT DEVELOPABLE • Surfaces (16 hrs) • Translatorial Surfaces • Ruled Surfaces • Helical Surfaces

49. Pro/Engineer • Surfaces (16 hrs) • Bézier Surfaces

50. AutoDesk INVENTOR MATHEMATICA Durchdringungskurve besteht aus zwei Ästen. PRO/ENGINEER • Intersection of surfaces (6 hrs)