Course Name Code Semester T+U Hours Credit ECTS
Spherical Conic Sections MAT 630 0 3 + 0 3 6
Precondition Courses <p>Completed master&#39;s degree in geometry</p>
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Dr.Öğr.Üyesi ENGİN CAN
Course Lecturers
Course Assistants
Course Category Field Proper Education
Course Objective

The aim of this course is to present some similarities and comparisons with spherical geometry theories on the basis of some geometry concepts, and to create new perspectives. Applications how geometric designs of technologies such as Global Positioning System (GPS) are created by using projective geometry concepts will be given.

Course Content

To provide the opportunity for similarity and comparison with the theories of spherical geometry, with the theories of classical planar geometry, the following resources are to be interpreted in order to locate and investigate the bases of advanced projective geometry topics.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Lecture, Group Study, Brain Storming, Self Study, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Spherical coordinates, Large circles and spherical distance
2 Angles, Triangles on the sphere, The spherical Pythagoras, Formulas of the spherical triangles
3 Formulas of the spherical triangles, The Gnomonic Projection, The spherical conic sections, The spherical ellipse and hyperbola
4 The spherical elliptical conic section, The Construction of De La Hire
5 Projective design of conic sections, Projectivities on the Euclidean plane
6 Projectivities on the sphere, Projective definition of conic sections
7 The Pascal’s theorem, Circles, Circuit and counterpoints, Circuit of plane and sphere conic sections
8 Funknavigation, Direction finding, Hyperbola method
9 Conic sections sample problems
10 The spherical peripheral angle theorem, Planar and Spherical peripheral angle
11 The reverse sections
12 Planar and spherical reverse sections
13 Ivory’s Theorem on the plane
14 Ivory’s Theorem on the sphere
Course Notes
Course Resources

[1] Bigalke H.G. (1984). Kugelgeometrie. Otto Salle Verlag. Frankfurt am    Main.

[2] Schupp H. (1988). Kegelschnitte. BI Wissenschaftsverlag. Mannheim

[3] Stachel H., Wallner J. (2003). Ivory’s Theorem in Hyperbolic Spaces. Technical Report No: 107. Institut für Geometrie, TU Wien.

[4] Tranacher H. (2006). Sphärische Kegelschnitte. Institut für Diskrete Mathematik und Geometrie. Technischen Universität Wien.

[5] Glaeser G., Stachel H., Odehnal B. (2016). The Universe of Conics. ISBN: 978-3-662-45449-7. Springer-Verlag Berlin Heidelberg.

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
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Performans Görevi (Seminer) 50
Total 100
1. Final 40
1. Yıl İçinin Başarıya 60
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
Performance Task (Seminar) 1 20 20
Final examination 1 30 30
Mid-terms 1 10 10
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6