(in Polish) Art of Geometry-Geometry of Art 1000-OG-EN-ART-GEO

The content of the course can be divided into three fields: basic geometry facts, fundamentals of using Geogebra, constructing patterns from the world of art and architecture based on different methods. The following topics will be intertwined throughout the course:
1. Examples of applications of geometry in art.
2. Basic geometric constructions in Geogebra.
3. Creating and managing tools in Geogebra.
4. Arithmetic of segments, constructability of angles, proportions and the golden ratio.
5. Exact and approximate constructions of regular polygons.
6. Isometries of the plane and their application to create geometric patterns.
7. Ornaments based on triangular, square circular and other grids.
8. Medallions, rosettes and other designs from Islamic mosques.
9. Examples of Coptic, Mughal, Chinese ornament.
10. Different Islamic patterns with a regular decagon based on one contour.
11. Filling patterns based on Persian ornaments. Persian ornaments with bands.
12. Alternative tessellations of patterns with a regular decagon.
13. Cosmatesque and guilloches, ornaments with circles, elements of programming in Geogebra.
14. Elements of Gothic ornament. Gothic rosettes.
15. Celtic braids and rosettes. Ribbon and interlacing patterns.
16. Tessellations, Penrose tessellations, Mr. Ammann's napkin.
17. Sangaku - illustrations for mathematical problems from Japanese temples. Use of inversion.