![]() ![]() ![]() The idea is similar to dividing a number by one of its factors. He experimented with practically every geometric shape imaginable and found the ones that would produce a regular division of the plane. Escher became obsessed with the idea of the “regular division of the plane.” He sought ways to divide the plane with shapes that would fit snugly next to each other with no gaps or overlaps, represent beautiful patterns, and could be repeated infinitely to fill the plane. The Dutch graphic artist was famous for the dimensional illusions he created in his woodcuts and lithographs, and that theme is carried out in many of his tessellations as well. These movements are termed rigid motions and symmetries.Ī good place to start the study of tessellations is with the work of M. The topic of tessellations belongs to a field in mathematics called transformational geometry, which is a study of the ways objects can be moved while retaining the same shape and size. We will explore how tessellations are created and experiment with making some of our own as well. There are countless designs that may be classified as regular tessellations, and they all have one thing in common-their patterns repeat and cover the plane. These two-dimensional designs are called regular (or periodic) tessellations. It may be a simple hexagon-shaped floor tile, or a complex pattern composed of several different motifs. Repeated patterns are found in architecture, fabric, floor tiles, wall patterns, rug patterns, and many unexpected places as well. In this section, we will focus on patterns that do repeat. What's interesting about this design is that although it uses only two shapes over and over, there is no repeating pattern. Notice that there are two types of shapes used throughout the pattern: smaller green parallelograms and larger blue parallelograms. The illustration shown above (Figure 10.101) is an unusual pattern called a Penrose tiling. Apply translations, rotations, and reflections.Transformation Videos: 3 videos demonstrating how to create a reflection tessellation, translation tessellation, and rotation tessellation (including how to do a graphite transfer or light table/window transfer for complex details).Īlso available in my Teachers Pay Teachers store.\)Īfter completing this section, you should be able to: Practice Tessellation Sheet: This page includes the base stencil for all three transformations shown in the videos and step-by-step sheets.Ħ. These instructions also match up with the included videos, which also demonstrate how to create them step-by-step.ĥ. Step-by-Step Direction Sheets: Three step-by-step instruction sheets with visuals showing how to create stencils for all three transformations. Practicing Transformations Worksheet: Worksheet asks students to reflect specific shapes over horizontal and vertical axes, translate shapes, and rotate shapes.Ĥ. Color Your Own Worksheets: Grid-filled pages that students can demonstrate how to draw translation, rotation, and reflection tessellations on.ģ. ![]() This PowerPoint includes animated slides, which make it easier for students to visualize the shape’s movements.Ģ. Escher (with a link to a interview he did), his influences, his artwork, and the three main types of transformations used in making tessellations – translation, rotation, and reflections. ![]() Tessellation PowerPoint: An introduction to what tessellations are, a brief history, M.C. If you are interested in this lesson, I have an incredibly awesome package posted up in my store. ![]()
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