Course Name Code Semester T+U Hours Credit ECTS
Motion Geometry MAT 531 0 3 + 0 3 6
Precondition Courses Students are assumed to be Transformations and Geometries.
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. MEHMET ALİ GÜNGÖR
Course Lecturers Prof.Dr. MEHMET ALİ GÜNGÖR,
Course Assistants Research assistants of geometry
Course Category
Course Objective The fundamental knowledge that are needed during students undergraduate and graduate education on motion geometry are taught. Furthermore, some different ways to solve the problems that they would come across on the subject are given.
Course Content Line-geometry, ruled surfaces, trajectory surfaces, one-parameter motions in line-space and ID- module, acceleration axes in Spatial motions, E. Study transformation of a circle.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She defines and calculates algebraic invariants of ruled surfaces in lines geometry. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
2 He/She constructs frame of trajectory surface, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
3 He/She defines 1-parameter dual spherical motion, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
4 He/She calculates algebraic invariants of 1-parameter dual spherical motion, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
5 He/She constructs Canonical Relative System of dual spherical motions. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
6 He/She generalizations Holditch and Steiner theorems for 1-parameter dual spherical motions, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
7 He/She defines closed ruled surfaces, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
8 He/She calculates velocities and acceleration in spatial motion, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
9 He/She formulates Bresse and inflection congruences of spatial motion. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Line-geometry
2 Ruled surfaces
3 Elements of trajectory and Pol tangent of a dual point
4 Principal Normal of the pol of a dual point and Using of Canonic Relative System
5 One-parameter motions in line-space and ID- module
6 Unit dual spherical motion and ruled surface theory
7 Generalizations of the Holditch theorem
8 Generalizations of the Steiner theorem
9 Midterm
10 The pitch of a closed ruled surface
11 Accelerations axes in spatial kinematics
12 Accelerations axes in spatial kinematics
13 Bresse and inflection congruences
14 Study map of a circle
Resources
Course Notes [1] Hacısalihoğlu, H.H., Hareket geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi yayınlar Mat. No.2,1983.
Course Resources [2] Hacısalihoğlu, H. H., Yüksek Boyutlu Uzaylarda Dönüşümler ve Geometriler, İnönü Üniversitesi, Temel Bilimler Fakültesi Yayınları, Mat. No.1, 1980.
[3] Hacısalihoğlu, H.H., Dönüşümler ve Geometriler, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,1998.
[4] Müller H. R., Kinematik dersleri, Ankara Üniv. Fen-fakültesi yayınları, Ankara
[5] Blaschke W., Zur Bewegungsgeometrie auf. Der kugel, S. B. Heildelberger. Wiss. Math. Nat. KI. No.2(1948)
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Ödev 30
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 1 15 15
Final examination 1 25 25
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6