However, more of the work is contributed to Mauritus Cornelius (M.C.) Escher in the artistic realm and Sir Roger Penrose in the mathematical context. No one knows for sure who put the first tessellation together for sure. Some created these new tessellations while others simply observed their natural occurrences to help explain some phenomenon's they were experiencing, later leading to many geometrical breakthroughs ("From Mathematics", 2016). Each civilization modifying the pattern slightly to help fulfill their culture and tradition. There have also been various tessellations found in Roman, Persian, Egyptian, Arab, Japanese, and Chinese art and architecture. This practice of using tessellations in sacred places later spread into Moor and Christian artwork. There are also tessellations that we can see in Greek and Muslim architecture, especially in their temples. Others claim to have found tiling pieces along the Nile River that date back between 12,000 and 18,000 years. These people would use clay tile patterns to create decorative features in their homes. What we do know is that they been traced as far back as the Sumerian civilization in 4000 B.C. No one is quite sure where tessellations first originated. These repeats can be either in shape, color, or both. When talking about the mathematical component, she goes on to say that mathematically, " tessellations are recognized as coverings of a plane or surface without any gapes in the ' tiling '." When we combine these two ideas, we recognize that we have a two-dimensional surface that has some sort of pattern or repeated shape which leaves no gaps. Robinson (2019) defines these as "shapes, patterns or figures that can be repeated to create a picture without any gaps of overlaps" when referring to the artistic side. They have slightly different definitions whether you're talking about a mathematical or artistic standpoint. What were these marvelous artistic patterns? How did they come to be? It's an interesting feeling you've never quite experienced before. The vibrant colors, simple yet intricate shapes, and soothing repetitious pattern both astound and calm you. You can't help but wonder, who created these patterns and why they chose to make them the way they did. Next, walking around the property you admire all the intricately designed carvings on the various columns and panels. The first thing you notice is the interesting tile pattern on the floor. Lizard tiles by Ben Lawson.Picture yourself in Northern Africa, on a tour of one of the mosques. Hexagonal and rhombic tessellations from Wikimedia Commons. Triangular tessellation from pixababy.If you want to try a more complicated version, cut two different squiggles out of two different sides, and move them both.Color in your basic shape to look like something - an animal? a flower? a colorful blob? Add color and design throughout the tessellation to transform it into your own Escher-like drawing. The shape will still tessellate, so go ahead and fill up your paper.Then move it the same way you moved the squiggle (translate or rotate) so that the squiggle fits in exactly where you cut it out. On a large piece of paper, trace around your tile. Tape the squiggle into its new location.It’s important that the cut-out lines up along the new edge in the same place that it appeared on its original edge.You can either translate it straight across or rotate it. Cut out the squiggle, and move it to another side of your shape.Draw a “squiggle” on one side of your basic tile.The first time you do this, it’s easiest to start with a simple shape that you know will tessellate, like an equilateral triangle, a square, or a regular hexagon. Here’s how you can create your own Escher-like drawings. Tessellations are often called tilings, and that’s what you should think about: If I had tiles made in this shape, could I use them to tile my kitchen floor? Or would it be impossible? The first two tessellations above were made with a single geometric shape (called a tile) designed so that they can fit together without gaps or overlaps. So we’ll focus on how to make symmetric tessellations. It’s actually much harder to come up with these “aperiodic” tessellations than to come up with ones that have translational symmetry. The Penrose tiling shown below does not have any translational symmetry. Many tessellations have translational symmetry, but it’s not strictly necessary. The idea is that the design could be continued infinitely far to cover the whole plane (though of course we can only draw a small portion of it). \)Ī tessellation is a design using one ore more geometric shapes with no overlaps and no gaps.
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