1 Institute of Geometry 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 Institute of Geometry SUPPLEMENTARY COURSES DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING GEOMETRY FOR MACHANICAL ENGINEERING

3 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY

4 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY 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.

5 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY

6 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY STUDENTS –First-year students with a high school diploma (Matura) without Descriptive Geometry BACKGROUND OF EXPERIENCE –Knowledge from mathematics at secondary school

7 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY ADDITIONAL INFORMATION –Semester hours (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 the winter semester (5 weeks)

8 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY STUDENTS - Students in a preparatory course (second-chance education) BACKGROUND OF EXPERIENCE - Knowledge from professional practice as draftsman, carpenter, plumber,...

9 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY ADDITIONAL INFORMATION -Semester hours (a total of 90 teaching units) -Course during the winter semester

10 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY -New curriculum in secondary schools -New curricula in: Mechanical Engineering Mechanical Engineering - Economics Architecture Civil Engineering -New curriculum in our supplementary courses

11 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY Projections Mathematical Resouces Special Surfaces CAD

12 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY 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 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY –Objects –Tools –Transformations –2D and 3D Constructions –Geometric Modeling (i.e. Boolean Operations) –Use of Auxiliary Coordinate-Systems

14 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY –Coordinate-Systems –Objects (Polygons, Circles, Conics ) –Objects (Prisms, Platonic Polyhedra, Pyramids) –Transformations

15 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY 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 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY Exam November Cube 2.Plane sections of a cone 3.Axonometric view of an object 4.Theoretical question about CAD-Packages

17 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY

18 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY Exam January Intersection of prisms 2.Shere and cylinder of revolution 3.Axonometric view of an object 4.Theoretical question about CAD-. Packages

19 Sybille Mick Institute of Geometry Zagreb, SUPPLEMENTARY COURSES IN DESCRIPTIVE GEOMETRY

20 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

21 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING 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 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING WEEKLY HOURS:Lecture and Laboratory : 4 hours STUDENTS:First-year students BACKGROUND OF EXPERIENCE: Knowledge from education at secondary school or a supplementary course in Descriptive Geometry

23 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING SKRIPT ONLINE DOCUMENTS AND MANUALS OTHER EQUIPMENT: Graphical Instruments

24 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING Topographic Projection ( hrs) Surfaces ( hrs) Intersection of surfaces ( hrs) Perspective Projection (4 + 4 hrs)

25 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING Concept of a lesson (H. J. Wresnik, S. Mick) Students work on their own (30 min): Students work with instruction (60 min): Manfred SPITZER: Lernen (2002).

26 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING Lesson: RAILWAY UNDERPASS Students work on their own (30 min): Training of terms Fill-in text THEORETICAL KNOWLEDGE Multiple choice Construction GRAPHICAL SKILLS (or Computation)

27 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

28 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

29 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

30 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

31 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING Lesson: RAILWAY UNDERPASS Students work with instructions (60 min): Materials: Description of the task Sheet to construct it on Hints to the solution Result

32 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

33 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

34 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

35 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

36 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

37 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING

38 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING INTERSECTION OF SURFACES – CONSTRUCTION AND COMPUTATION

39 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING PERSPECTIVE PROJECTION

40 Sybille Mick Institute of Geometry Zagreb, DESCRIPTIVE GEOMETRY FOR CIVIL ENGINEERING Obligatory attendence and Satisfactory performance in two tests and a final written examination

41 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING

42 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING 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 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING WEEKLY HOURS:Lecture: 2 hours Laboratory: 1 hour Tutorial: 1 hour (voluntary) STUDENTS:Second-year students STUDENTS´ PREREQUISITES: Knowledge from education at secundary school or a supplementary course in Descriptive Geometry

44 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING SKRIPT ONLINE-ADVISES SOFTWARE: Maple, ProE OTHER EQUIPEMENT: Graphical Instruments

45 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Mathematical foundation Curves and surfaces Intersection of surfaces

46 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Mathematical foundation (8 hrs) –Displacements 2D and 3D –Curves and Surfaces Figur 10: Der Krümmungskreis oskuliert die Raumkurve im Punkt P. k tPtP P M Krümmungskreis Krümmungsmitte Kurventangente Hauptnormale

47 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Surfaces (16 hrs) –Algebraic Surfaces (e.g. Surfaces of second order) –Cylinders and Cones –Surfaces of Revolution Pro/Engineer

48 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Surfaces (16 hrs) –Translatorial Surfaces –Ruled Surfaces –Helical Surfaces DEVELOPABLE NOT DEVELOPABLE

49 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Surfaces (16 hrs) –Bézier Surfaces Pro/Engineer

50 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Intersection of surfaces (6 hrs) AutoDesk INVENTOR Durchdringungskurve besteht aus zwei Ästen. MATHEMATICA PRO/ENGINEER

51 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING Mathematical foundation with Maple Curves and surfaces with Maple and ProE Intersection of surfaces

52 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING LABORATORY: Submission of three assignements TUTORIAL: Satisfactory performence in four tests LECTURE: Final written and oral exam

53 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING

54 Sybille Mick Institute of Geometry Zagreb, GEOMETRY FOR MECHANICAL ENGINEERING