Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMG1011 | Topics in Geometry II (for teachers education) |
| Teaching Staff in Charge |
Assoc.Prof. BLAGA Paul Aurel, Ph.D., pablaga cs.ubbcluj.ro |
| Aims |
|
The aim of the course is to familiarize the students with the theory of geometric constructions in the Euclidean plane, realized with the compass and the ruler, as well as with different selections of instruments. At the end of the course, the students should be able to approach correctly a construction problem and tu apply the methods described in the course for its solution. |
| Content |
|
1.Fundamentals of the geometric constructions@ theory
2.Methods for solving problems of geometric constructions and geometric loci 3.Geometric constructions realized only with the ruler or only with the compass 4.Geometric constructions with other instruments 5.Applications of the Galois theory to the theory of geometric constructions 6.Dividing the circle 7.The classical problems of antiquity (the impossibility of the solution with the ruler and the compass only, approximate solutions) |
| References |
|
1.Adler, A.: Theorie der geometrischen Konstruktionen, Teubner, 1906
2.Alexandrov, I..: Probleme de construcţii geometrice, Editura Tehnică, 1951 3.Argunov, B., Balk, M.: Construcţii geometrice în plan (în limba rusă), ed. a 2a, Moscova, 1957 4.Beskin, N. ş.a.: Principiile generale ale construcţiilor geometrice (în limba rusă), în Enciclopedia de Matematică Elementară, vol. 4, Moscova, 1963, pag. 159 – 204 5.Enriques, F.: Questioni riguardanti la geometria elementare, Bologna, 1900 6.Howie, J.: Fields and Galois Theory, Springer, 2005 7.Isaacs, M.: Algebra: A Graduate Course, Wadsworth Inc., 1995 8.Manin, J.: Asupra rezolvabilităţii problemelor de construcţii cu ajutorul riglei şi a compasului (în limba rusă), în Enciclopedia de Matematică Elementară, vol. 4, Moscova, 1963, pag. 205 – 227 9.Petersen, J.: Methodes et theories pour la resolution des problemes de constructions geometriques, ed. a 2a, Gauthier-Villars, 1892 10.Toth, A.: Noţiuni de teoria construcţiilor geometrice, Editura didactică şi pedagogică, 1963 |
| Assessment |
|
Final written exam (70%), homeworks and presentations (30%) |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |