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Seminar 2 - Selected topics in geometry

Code: 31447
ECTS: 3.0
Lecturers in charge: doc. dr. sc. Tomislav Pejković - Lectures
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Seminar 30
* Load is given in academic hour (1 academic hour = 45 minutes)
The main aim of this seminar is to enhance student's ability for individual and team work.
Topics will cover some elementary geometry topics which are not studied in other courses, but future high school teachers are expected to be familiar with. The topics are chosen to promote the most important didactical principles.

Students will be divided in teams of three students. Each team will choose a topic from elementary geometry and, after wide search for additional information from different sources, prepare a seminar paper (essay). At the end they will give a presentation about the topic using different means (posters, computer aided presentation etc).
The topics are:
Spherical geometry. Basic concepts of geometry on sphere. Transformations. Spherical triangles and its properties. The Gauss-Bonnet formula. Applications.
Polygons. Constructions of regular polygons. The Gauss theorem. Drawing methods for regular polygons.
Characteristic points in triangle. The four characteristic points. Other characteristic points in triangle: isogonal points, Brocard points, Lemoine point, Gergonne and Nagel points, Tarry point etc.
Circles and triangles. Circles related to triangle: incircle, circumcircle, excircle, Tucker circles, Lemoine circles, Taylor circle, Feuerbach circle, etc.
  1. B. Pavković, D. Veljan: Elementarna matematika 1
  2. B. Pavković, D. Veljan: Elementarna matematika 2
  3. D. Palman: Trokut i kružnica
  4. P. J. Ryan: Euclidean and non-Euclidean geometry
  5. D. W. Henderson: Experiencing geometry on plane and sphere
Prerequisit for:
Enrollment :
Passed : Analytic geometry
Passed : Elementary geometry
4. semester
Mandatory course - Regular study - Mathematics Education
Consultations schedule: