Designing and Drawing Tessellations

Where art meets mathematics in a tessellation

Tessellations whose individual tiles are lifelike motifs, in the tradition of M.C. Escher, are a 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.

A tiling is a repeating pattern of shapes that covers a surface with no gaps or overlaps. A triangle, a square and regular hexagons tessellate on their own. The difference lies in reshaping such a tile into a bird, a fish or a figure that still fits its neighbours.

What the book teaches about making a tessellation

Written by mathematical artist Robert Fathauer, Designing and Drawing Tessellations shows you how to make one, from the first idea to the finished design. Here is what it covers:

• History and background: the story behind art based on tessellations.
• The required geometric concepts, focusing on transformations and symmetry: a squiggly line drawn on one edge, then moved by translation to the opposite edge, keeps the tile fitting.
• Numerous tips and techniques on the artistic aspects of creating tessellations, material not found in any other source.
• A step-by-step illustrated example describing the process of designing and drawing a tessellation in detail, which works as a full tutorial.
• Dozens of different templates for creating a wide variety of tessellations.

Tessellation activities for the classroom and home

The book is designed for use either by individuals or in a classroom. Each chapter contains activities designed for a classroom setting: a teacher can build a STEM or art lesson directly from the chapter in hand. Students and adults alike enjoy creating mathematical art, and it builds spatial reasoning alongside creativity.

In practice, it is best suited to a secondary class or an adult learner who is comfortable with a ruler and pencil. Pick one template, trace it and repeat it across a sheet. You will see a mosaic of interlocking motifs take shape on the page.