COURSE AIMS AND OBJECTIVES:
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.
COURSE DESCRIPTION AND SYLLABUS:
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.