Adventures On Paper

Edited by Kristóf Fenyvesi, Ilona Oláhné Téglási and Ibolya Prokajné Szilágyi

Publisher: Eszterházy Károly College, Eger, 2014

ISBN: 978-615-5297-25-0

This publication is a pedagogical toolkit, which presents hands-on materials and detailed methodological descriptions for the realization of almost forty interactive math-art workshops in the classroom. A number of significant international representatives of visual mathematics, mathematical art and experience-centered mathematics teaching have contributed and we have tried to cover a wide variety of topics. Most of the activities we selected can be completed with paper or cardboard on a cost-effective way and equipment readily-available in most educational institutions such as scissors and colouring pencils, and, at most, a photocopier.

We hope that the teachers who use our toolkit will succeed in encouraging their students to see mathematics as a joyful endeavour rather than the dry and boring subject many believe it to be. Moreover, we hope that this collection is adopted as a handbook not just by math teachers, but also by art teachers wishing to illuminate the links between the two disciplines of art and math.

GeoGebra Action Package (GAP) for the ADVENTURES ON PAPER exercise book

Please note, that you need to install GeoGebra on your computer to run the following files. GeoGebra is an open source software freely available for non-commercial users. You can download Geogebra from here: https://www.geogebra.org/download

Patterns, Symmetry, Modularity and Tile Games by Slavik Jablan and Ljiljana Radovic [instructions for the GeoGebra files] (Ex. 1: Practice Frieze symmetries!, Ex. 2: Construct labyrinths!) [geogebra file - Ex. 1] [geogebra file - Ex. 2]

Decoration of Polyhedra using Escher-like Tessellations by Robert Fathauer [instructions for the GeoGebra files] (Ex. 1: Constructing rays in GeoGebra, Ex. 2: Squids and other rosettes in the fifth-order) [geogebra file - Ex. 1] [geogebra file - Ex. 2]

Tangram-type Games Developing the Concept of Area and Volume by Ilona Oláhné Téglási [instructions for the GeoGebra files] [compressed geogebra files]

Möbius Strip and Frieze Symmetries by Eleonóra Stettner [instructions for the GeoGebra files] (Ex. 1: Interesting features of Moebius strip, twisted strips and their limits, Ex. 2: Make symmetric and asymmetric graphs!) [geogebra file - Ex. 1] [geogebra file - Ex. 2]

The Polygonal Technique in Islamic Geometric Design by Jay Bonner [instructions for the GeoGebra file] (Semi-regular Archimedean tiling) [geogebra file]

Arabesques and Quasicrsystals by Jean-Marc Castera [instructions for the GeoGebra files] (Ex. 1: Constructing golden section and golden triangle, Ex. 2: Construction of a rosette from rhombuses) [geogebra file - Ex. 1] [geogebra file - Ex. 2]

Decorating Regular Polyhedra Using Historical Persian Interlocking Star Polygonal Patterns by Reza Sarhangi [instructions for the GeoGebra file] (Constructing Mirza Akbar’s decorated pentagon) [geogebra file]

Impossible Objects, Paradox Figures by Tamás F. Farkas [instructions for the GeoGebra files] [geogebra file - Ex. 1] [geogebra file - Ex. 2]

Let us play Native American! by Georg Glaeser [instructions for the GeoGebra file] [geogebra file]

Design Anamorphosis in the Classroom by Kristóf Fenyvesi and Ildikó Szabó [instructions for the GeoGebra file] [geogebra file]

3D Fractal Workshops by Dirk Huylebrouck [instructions for the GeoGebra files] (Ex. 1: Creating Koch-snowflake in GeoGebra, Ex. 2: Construct the Africa fractal) [geogebra file - Ex. 1] [geogebra file - Ex. 2]

“Slide-Together” Geometric Paper Constructions by George Hart [instructions for the GeoGebra file] (Construction of pentagram template in Geogebra) [geogebra file]

Leonardo’s Elevated Polyhedra Models by Rinus Roelofs [instructions for the GeoGebra file] (Leonardo’s graphics in GeoGebra) [geogebra file 1] [geogebra file 2]

Mathematical Adventures in Origami by Krystyna Burczyk and Wojtek Burczyk [instructions for the GeoGebra files] [geogebra file - Ex. 1] [geogebra file - Ex. 2]

All Geogebra applications and instructions were made by Eleonóra Stettner and the Tempus Geogebra Team.