Elementary geometry

2022/2023
Programme:
Mathematics Education
Year:
2 year
Semester:
first
Kind:
mandatory
ECTS:
6
Language:
slovenian
Hours per week – 1. 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

Damjan Kobal:
KOBAL, Damjan. Technology and simple math ideas inspire teaching. V: ICME - 12 : the 12th International Congress on Mathematical Education, July 8-15, 2012, COEX, Seul, Korea. Cheongju: Korea National University of Education, 2012, 7 str. [COBISS-SI-ID 17151577]
KOBAL, Damjan, et al. Integrating algebra and geometry with complex numbers. V: International Seminar in Mathematics Education 2011. Park City: Park City Mathematics Institute - Institute for Advanced Study, cop. 2013, 9 str. [COBISS-SI-ID 17152345]
KOBAL, Damjan. Iluzija objektivnosti ali objektivnost odgovornosti. Obzornik za matematiko in fiziko, ISSN 0473-7466, 2007, letn. 54, št. 1, str. 18-28. [COBISS-SI-ID 14302297]
iv) KOBAL, Damjan. Inner product space and circle power. Publicationes mathematicae, ISSN 0033-3883, 2012, vol. 81, fasc. 1-2, str. 1-9. [COBISS-SI-ID 16336473]

Sašo Strle:
STRLE, Sašo. Bounds on genus and geometric intersections from cylindrical end moduli spaces. Journal of differential geometry, ISSN 0022-040X, 2003, vol. 65, no. 3, str. 469-511. [COBISS-SI-ID 13135193]
OWENS, Brendan, STRLE, Sašo. A characterization of the Z [sup] n [oplus] Z([delta]) lattice and definite nonunimodular intersection forms. American journal of mathematics, ISSN 0002-9327, 2012, vol. 134, no. 4, str. 891-913. [COBISS-SI-ID 16408153]
GRIGSBY, J. Elisenda, RUBERMAN, Daniel, STRLE, Sašo. Knot concordance and Heegaard Floer homology invariants in branched covers. Geometry & topology, ISSN 1364-0380, 2008, vol. 12, iss. 4, str. 2249-2275 [COBISS-SI-ID 14892121]