1. komponenta

Lecture type	Total
Lectures	30
Exercises	30
Seminar	15

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
This course is a continuation of the course Elementary geometry 1. The aim of the course is to systematize and expand knowledge of elementary geometry of the plane and space.

COURSE DESCRIPTION AND SYLLABUS:
Trigonometry: right triangle trigonometry, trigonometric functions. The Sine and Cosine rules. Planimetric derivatives of addition formulas.
Isometries: Axial and central symmetry, rotation, translation - various definitions. Plane isometries and their properties. Sliding symmetry. Group of isometries. Basic theorem on plane isometries. Constructions using isometries.
Homothety: definition and basic properties. Composition of two homotheties. Constructions using the homothety method. Proofs by homothety - Feuerbach circle and Euler line
Power of a point with respect to a circle, radical axis of two circles, radical center of three circles
Inversion of a plane: definition, properties (images of lines and circles). Apollonius' problem. Proofs by inversion - Ptolemy's theorem and Ptolemy's inequality
Space geometry (stereometry):
Points, lines, planes and their mutual relations in space. Parallelism, perpendicularity and angle. Distance.
Geometric solids. Polyhedra. Euler's formula for polyhedra. Plato's solids. Curved solids. Volume and surface area. Cavalieri principle.
Isometries of space
Additional topics are covered at the seminars, e.g. algebraic method for solving construction problems, Simson line, Gergonne and Nagel point, Feuerbach point, Brahmagupta's theorem, classic constructive problems (duplication of a cube, angle trisection, and squaring a circle), constructibility of regular polygons, Mohr-Mascheroni constructions...

1. Elementarna matematika 1, B. Pavković, D. Veljan, Školska knjiga, Zagreb, 2004.
2. Elementarna matematika 2, B. Pavković, D. Veljan, Školska knjiga, Zagreb, 1995.
3. Geometrijske konstrukcije, D. Palman, Element, Zagreb, 1996.
4. Trokut i kružnica, D. Palman, Element, Zagreb, 2004.

Enrollment :
Passed : Elementary geometry 1

Mandatory course - Regular study - Mathematics Education