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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
SPHERICAL CONIC SECTIONS 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 SECMELI
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.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - 1 - 8 - 10 - 14 - C - F -
Öğretim Yöntemleri: 1:Lecture 8:Group Study 10:Brain Storming 14:Self Study
Ölçme Yöntemleri: C:Homework F:Performance Task

Ders Akışı

Hafta Konular ÖnHazırlık
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
6 Projectivities on the sphere, Projective definition of conic sections
5 Projective design of conic sections, Projectivities on the Euclidean plane
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.


Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
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 follows the necessary technological developments in his/her field, and s/he uses them. X
10 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 50
PerformansGoreviSeminer 1 50
Toplam 100
Yıliçinin Başarıya Oranı 60
Finalin Başarıya Oranı 40
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(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
Mid-terms 1 10 10
Assignment 0 0 0
Performance Task (Seminar) 1 20 20
Final examination 1 30 30
Toplam İş Yükü 156
Toplam İş Yükü /25(s) 6.24
Dersin AKTS Kredisi 6.24
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