Art of Geometry-Geometry of Art

The aim of the course is to prepare students to apply geometric constructions in creating intricate patterns derived from architecture and art with the use of the computer program. For this purpose, fundamental geometric constructions, together with some elementary facts, as well as the basics of Geogebra software, will be presented. During the exercise classes, students will prepare projects inspired by concrete geometric patterns coming from the world of Islamic, Celtic or Gothic art and others. Sample projects that will be created as part of the classes can be found at instagram profile geometryofart: https://www.instagram.com/geometryofart/

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.

Basic literature:

1. H. Fukagawa, T. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press, 2008.

2. R. Hartshorne, Geometry : Euclid and Beyond, New York, Springer, 2000.

3. M. Majewski, Islamic Geometric Ornaments in Istanbul, MATHPAD 2010 Post-conference Materials, Toruń, 2011.

4 M. Majewski, Practical Geometric Pattern Design -Decagonal Patterns in Persian Traditional Art, Independently published, 2021.

5. M. Majewski, Practical Geometric Pattern Design - Geometric Pattern in Islamic Arts, Wydawnictwo Aksjomat, 2019.

6. M. Majewski, Practical Geometric Pattern Design - Lessons from the Topkapi Scroll, Independently published, 2021.

7. M. Majewski, Understanding Geometric Pattern and its Geometry. Part 1-8, series of papers published mainly in The Electronic Journal of Mathematics and Technology.

8. M. Majewski, Ribbon Patterns with Geometry Software, The Electronic Journal of Mathematics and Technology , 2018, 12(3):322-342.

Supplementary literature:

1. H. Conway, H. Burgel, C. Goodman-Strauss, The Symmetries of Things, Wellesley, A K Peters / CRC Press, 2008

2. H. S. M. Coxeter, Introduction to Geometry, Wiley; 2nd edition, 1991.

3. C. Horne, Geometric Symmetry in Patterns and Tilings, Cambridge, England: Woodhead Publishing Ltd., 2000.

4. O. Jones, The Grammar of Ornament : A Visual Reference of Form and Colour in Architecture and the Decorative Arts - The complete and unabridged full-color edition, Princeton, NJ : Princeton University Press, 2016.

5. M. Majewski, O geometrii i sztuce: między Wschodem i Zachodem, Wydawnictwo Aksjomat, Toruń, 2012.

6. M. Majewski, O geometrii i sztuce: sztuka konstrukcji geometrycznych, Wydawnictwo Aksjomat, Toruń, 2013.

7. M. Majewski, O geometrii i sztuce: gereh i geometria w sztuce islamu, Wydawnictwo Aksjomat, Toruń, 2017.

Passing the subject with a grade based on the preparation of a graphic designs in a computer program and its presentation.

not applicable