Elementary geometry

2018/2019
Programme:
Mathematics Education
Year:
2 year
Semester:
second
Kind:
mandatory
ECTS:
6
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 2. semester:
Lectures
3
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)

Euklid's Elements. Hilbert's axioms – overview of basic ideas of Euclidean and Hyperbolic (plane) geometry. Basics of Spheric geometry. Isomeries, symetries, symilarity and congruency. Tales theorems. Euclid's circle theorems. Chord and tangent quadrilaterals. Power of a point. Inversion. Poincaré models of the hyperbolic plane. Hyperbolic trigonometry. Apollonian circle and Apollonian problem. Simson's line. Stewart's and Ceva's theorems. Euler's line. Nine point circle. Menelaus, Pappus and Desargues theorems. Fagnano's problem. Trilinear coordinates. Morley's theorem. Equilaterals and angle trisection. Platon's solids. Polyhedron's and Euler's formula.

Readings

N. Altshiller-Court: College Geometry, 2nd edition, Dover Publications, Mineola, New York, 2007.
B. Artmann: Euclid - The Creation of Mathematics, Springer, New York, 2001.
H. S. M. Coxeter: Introduction to Geometry, 2nd edition, John Wiley & Sons, New York, 1989.
H. Dörrie: 100 Great Problems of Elementary Mathematics : Their History and Solution, Dover Publications, New York, 1982.
M. J. Greenberg: Euclidean and Non-Euclidean Geometries: development and history, Freeman, New York, 1973.
S.Lang, G. Murrow: Geometry: a high school course, Springer, New York, 1983.
D. Pagon: Osnove evklidske geometrije, DZS, Ljubljana, 1995.

Objectives and competences

Student acquires the basic knowledge and skills in elementary geometry. Solving the elementary problems, student enhances his or her mathematical thinking and comprehension. The course by its content and methods of teaching deepens a prospective teacher's essential mathematical knowledge and skills.

Intended learning outcomes

Knowledge and understanding:
Knowledge and comprehension of essential concepts and definitions of elementary geometry and acquired ability to use these methods in elementary mathematical problems.

Learning and teaching methods

Lectures, tutorial sessions, individual consultations

Assessment

Written exam
Oral exam

Lecturer's references

LAVRIČ, Boris. The isometries of certain maximum norms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2005, vol. 405, str. 249-263. [COBISS-SI-ID 13679961]
LAVRIČ, Boris. Vsote praštevil in vsote njihovih kvadratov. Obzornik za matematiko in fiziko, ISSN 0473-7466, 1996, let. 43, št. 5, str. 161-167. [COBISS-SI-ID 7003737]
LAVRIČ, Boris. Parketiranje ravnine s konveksnimi mnogokotniki. Obzornik za matematiko in fiziko, ISSN 0473-7466, 1980, let. 27, št. 4, str. 97-101, graf. prikazi. [COBISS-SI-ID 8007513]