Tessellations Books

These books are all written by Tessellations founder Robert Fathauer and published by Tessellations.

Designing and Drawing Tessellations

Tessellations in which the individual tiles are lifelike motifs are a fun and fascinating combination of art and mathematics. At first glance, the creation of these intriguing designs can appear to be a complete mystery. Once the mathematical underpinnings are understood, however, designing them is a skill anyone can master.

Designing and Drawing Tessellations presents everything needed for mastering this art. History and background on the topic are followed by descriptions of the required geometric concepts, focusing on transformations and symmetry. Numerous tips and techniques on the artistic aspects of creating tessellations are also presented, material not available from any other source. A step-by-step illustrated example describes in detail the process of designing and drawing a tessellation. Finally, dozens of different templates are included for creating a wide variety of different tessellations.

Designing and Drawing Tessellations is designed for use either by individuals or in a classroom. Each chapter contains activities designed for a classroom setting. Students and adults alike love tessellations - they make math fun while encouraging creativity!

Click on the following links to download sample pages from the book in pdf format:
Student worksheet example
Tessellation template example

Item no. 193; ISBN 978-0-9802191-3-5. 8-1/2" x 11", 142 pages. Suggested retail price: \$24.95.

Designing and Building Tessellated Polyhedra

Polyhedra allow geometric shapes in the plane to become solids in our three-dimensional world. Tessellations in which individual tiles are lifelike motifs are a fun combination of art and mathematics. Designing and Building Tessellated Polyhedra brings these two fascinating topics together a for hands-on learning experience rich in math content. Nets for 24 different polyhedra, including all of the Platonic and Archimedean solids, are presented both with and without tessellations applied to them. This allows polyhedra to be built with ready-made designs that can be colored if desired, or printed in beautiful color using the included CD. Another option is building undecorated polyhedra that have the names and key properties printed on them. Yet another possibility is to use templates to design new tessellations that can be applied to the polyhedra. The book also contains background on polyhedra and templates for tessellated cones, cylinders, and Mšbius strips. For classroom use, ten activities with worksheets, designed to address ten different specific Common Core State Standards for Mathematics are included as well.

Click on the following links to download sample pages from the book in pdf format:
Classroom activity example
Polyhedron net example

Item no. 198; ISBN 978-1-938664-02-1. 8-1/2" x 11", 111 pages, with CD. Suggested retail price: \$29.95.

Tessellations Around the World

Tessellations are collections of shapes that fit together to cover a surface without gaps or overlaps. They play important roles in the animal world, the behavior of materials, the decorative arts, architecture, and more.

Tessellations Around the World contains nearly 100 photographs of tessellations found in nature and in synthetic objects. A line drawing of the tessellation, a map showing its location, and a series of questions accompany 50 of the photographs. In addition to math questions, there is one question for each page relating to geography or culture. The book also contains chapters on tessellation basics, symmetry in tessellations, and tessellations in the real world. The tessellations are grouped by geographical region, and there is an introduction to the tessellations of each region.

Tessellations Around the World is designed for use either by individuals or in a classroom setting. Many of the questions in the book are designed to address specific Common Core State Standards for Mathematics. Tessellations Around the World will help you or your students recognize and appreciate mathematics in the world around us, while reinforcing geometry and problem solving skills.

Click on the following links to download sample pages from the book in pdf format:
Sample page 1
Sample page 2

Item no. 199; ISBN 978-1-938664-13-7. 8-1/2" x 11", 92 pages. Suggested retail price: \$19.95.

Fractal Trees

Fractals are objects that exhibit similar structure on different scales. They abound in the natural world, from clouds to mountains, coastlines to trees, even our own circulatory system.

In this volume, by combining photographic imagery with iteration, the mathematical process at the heart of fractals, Robert Fathauer explores his unique vision of a nature that is even more fractal than the real world. These creations include a fern-like tree built from the stem of a rose bush, an infinite collection of spirals formed from the skeleton of a cholla cactus, and a tree whose outline resembles a maple leaf.

Thirteen different trees are shown in two page spreads, an example of which can be seen here. Six randomized fractal trees are shown as well, two of which are shown here. The book also includes a section on the method used to create the trees and notes on the individual trees.

In "Fractal Trees", mathematics and art unite to yield images that are intricate and complex, while retaining simplicity and grace. Included with the book are four classroom worksheets that teachers can copy, covering branching of fractal trees, trees in nature, infinite series, and fractal dimension.

Classroom worksheets tied to the book are available for download.

Item no. 196; ISBN 978-0-9846042-2-7. 8-1/2" x 11", 52 pages. Suggested retail price: \$19.95.

Geometric Shapes Activity Book

This book contains two pages of background material about geometric shapes, an activities example page, plus two dozen 8.5" x 11" pages of different geometric shapes. Each shape is incorporated in a larger drawing showing an example of the shape in the real world or its use in a geometric design. There are six activities that may be performed for each page:

1. Coloring the large geometric shape and drawing incorporating it.
2. Drawing the geometric shape, first by using the dots provided in the lower right corner for guidance, and then freehand.
3. Writing out the name of the shape, and learning to pronounce and spell it.
4. Coloring the tessellation example.
5. Marking the rotational and mirror symmetries of the shape on the drawing in the upper right corner.
6. Measuring the dimensions of the shape in the upper right drawing and using them to calculate the perimeter or area.

Item no. 195; ISBN 978-0-9802191-6-6. Suggested retail price: \$9.95.

Regular Polygon Tessellations Activity Book

This book contains two pages of background material about tessellations, an activities example page, plus two dozen 8.5" x 11" pages of tessellations in which the individual tiles are regular polygons. There are five activities that may be performed for each page:

1. Identifying the different types of tiles in the design;
2. Identifying the unit cell for the design (the group of tiles that can be repeated to cover the plane);
3. Marking the different types of symmetry the design possesses;
4. Identifying the distinct types of vertices in the design;
5. Coloring the design.

Item no. 192; ISBN 978-0-9802191-2-8. Suggested retail price: \$9.95.

Lifelike Tessellations Activity Book

This book contains two pages of background material about tessellations, an activities example page, plus two dozen 8.5" x 11" pages of original Escher-like designs. There are five activities that may be performed for each page:

1. Identifying the different types of tiles in the design;
2. Identifying the unit cell for the design (the group of tiles that can be repeated to cover the plane);
3. Marking the different types of symmetry the design possesses;
4. Drawing the geometric grid on which the design is based;
5. Coloring the design.

Item no. 191; ISBN 978-0-9802191-1-1. Suggested retail price: \$9.95.

Polyhedra Activity Book

This book contains two pages of background material about polyhedra, an activities example page, plus two dozen 8.5" x 11" pages of different polyhedra, including all eighteen Platonic and Archimedean Solids. There are six activities that may be performed for each page:

1. Identifying the number and different types of polygons in the polyhedron;
2. Counting the number of vertices, faces, and edges in the polyhedron;
3. Writing out the name of the polyhedron and learning to pronounce it;
4. Marking the different types of symmetry the polyhedron possesses;
5. Drawing the polyhedron by connecting dots;
6. Coloring the polyhdedron.

Item no. 194; ISBN 978-0-9802191-5-9. Suggested retail price: \$9.95.