Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMG1010 | Topics in Geometry I (for teachers education) |
| Teaching Staff in Charge |
Lect. VACARETU Daniel, Ph.D., vacaretu math.ubbcluj.ro |
| Aims |
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The purpose of the course is to go thoroughly into basic elements of the plane geometry: the triangle, the quadrilateral, the circle. At the end of the course, the students will be able to correctly identify the plane geometric figures and their connections, also to combine classical geometric results, in order to solve several types of problems. |
| Content |
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The triangle. Associated lines for a triangle: the medians, the altitudes, the bisectors, the perpedincular bisectors, the symmedians. Associated points: the centroid, the orthocenter, the inncenter, the circumcenter, the centers of the exinscribed circles, the Gergonne point.
The quadrilateral. The square, the rectangle, the rhombus, the parallelogram, the trapezoid. The arbitrary quadrilateral. The circle: arcs, chords, tangent lines, lengths, arias. The congruence and the similarity of geometric figures. The congruence of the triangles. The similarity of the triangles. Congruent polygons and similar polygons. Inscribed, exinscribed and circumscribed circles. Convexe polygons. Regular polygons. Inscriptibil quadrilaterals. Circumscriptible quadrilaterals. Concurrence and collinearity. The Menelaus@ theorem. The Ceva@s theorem. Metric relations. Solving the right-angled triangle. The computations of several lines associated to a triangle. Arias. Computation of arias. Geometric locuses. Geometric inequalities. Maxim and minimum in geometry. Combinatorial problems in geometry. Applications of projective geometry in triangle geometry. |
| References |
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1. Andrica, D., Varga, Cs., Văcăreţu, D., Teme şi probleme alese de geometrie, Editura
Plus, Bucureşti, 2002 2. Barbu, C., Teoreme fundamentale din Geometria Triunghiului, Editura UNIQUE Bacau,2008 3. Drăghicescu, I.C., Masgras, V., Probleme de geometrie, Editura Tehnică, Bucureşti,1987 4. Hadamard, J., Lecţii de geometrie elementară: geometrie plană, Editura Tehnică, Bucureşti,1960 5. Lalescu, T., Geometria triunghiului, Editura Tineretului, Bucureşti,1959 6. Mihăileanu, N.N., Lecţii complementare de geometrie, Editura Didactică şi Pedagogică, Bucureşti, 1976 7. Nicolescu, L., Boskoff, V., Probleme practice de geometrie, Editura Tehnică, Bucureşti, 1990 8. Pimsner, M., Popa, S., Probleme de geometrie elementară, Editura Didactică şi Pedagogică, Bucureşti, 1979 9. Ţiţeica, G., Culegere de probleme de geometrie, Editura Tehnică, Bucureşti, 1960 |
| Assessment |
|
The final grade is calculated as:
60%-written final exam 20%-individual homeworks, during the semester 20%-student activity in seminars, during the semester |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |