Cool Tessellation Ideas Index Cards

When exploring the world of tessellations, it's essential to understand that when a number divides another number evenly, there are no remainders - just like how shapes can divide or fill the plane without any gaps. M.C. Escher took this concept to new heights by using various shapes, including figures, faces, animals, fish, and more, to achieve his goal of creating beautiful patterns that could be repeated infinitely.

In a similar manner, dividing a number by one of its factors can help us understand the idea behind tessellations. By experimenting with different geometric shapes, Escher discovered those that would produce regular divisions of the plane. He sought ways to divide the plane using shapes that fit snugly next to each other without gaps or overlaps, creating beautiful patterns and symmetries.

Escher's work in tessellations is a testament to his fascination with the 'regular division of the plane.' His dimensional illusions in woodcuts and lithographs are carried over into many of his tessellations. Rigid motions and symmetries are essential elements in creating these designs.

To begin studying tessellations, it's beneficial to explore the work of M.C. Escher, who is renowned for his dimensional illusions. Tessellations belong to a field of mathematics called transformational geometry, which involves studying the ways objects can be moved while retaining their shape and size.

Regular (or periodic) tessellations are two-dimensional designs that repeat patterns and cover the plane. These designs can range from simple hexagon-shaped floor tiles to complex patterns composed of multiple motifs. Repeated patterns are found in various areas, such as architecture, fabric, floor tiles, wall patterns, rug patterns, and even unexpected places.

In this section, we will focus on patterns that do repeat, showcasing the beauty and complexity of tessellations. For instance, notice how a simple pattern using only two shapes - smaller green parallelograms and larger blue parallelograms - can create an intricate design without repeating itself. The Penrose tiling (Figure 10.77) is another unusual pattern that uses translations, rotations, and reflections to achieve its unique design.

Learning Objectives:

By the end of this section, you should be able to:

* Apply translations, rotations, and reflections in creating tessellations

* Identify regular (or periodic) tessellations and their applications in various fields

In conclusion, tessellations are a fascinating world that offers endless possibilities for creativity and exploration. With this introduction to cool tessellation ideas index cards, you can start experimenting with different shapes and patterns to create your own unique designs.

Cool tessellation ideas index cards