Syllabus
Different proofs of Pythagoras' theorem, Euclid's theorems and other important theorems.A quadrilateral and its properties, quadrilaterals circumscribed and inscribed into a circle and their use in exercises. A circle and its use in geometric problems.Means (arithmetic, geometric, harmonic, quadratic) and their geometric interpretation.Metric properties of planar and spatial objects.
Use of congruencies and similarities in planar and spatial geometric problems.Regular and semiregular polyhedra.
Annotation
The subject extends Synthetic Geometry I and II. Historic and modern proofs of important synthetic geometry theorems are shown to students.
Geometric problems from higher mathematical competitions are discussed.