| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Spherıcal Conıc Sectıons | MAT 630 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Completed master's degree in geometry |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Dr.Öğr.Üyesi ENGİN CAN |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | 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. |
| Dersin İçeriği | 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. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Lecture, Group Study, Brain Storming, Self Study, | Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 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 |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | [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. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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 | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 50 |
| 1. Performans Görevi (Seminer) | 50 |
| Toplam | 100 |
| 1. Final | 40 |
| 1. Yıl İçinin Başarıya | 60 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| 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 |
| Toplam İş Yükü | 156 | ||
| Toplam İş Yükü / 25 (Saat) | 6,24 | ||
| Dersin AKTS Kredisi | 6 | ||