We then start to move up in complexity of both the patterns and interactions of the shapes we use. These are just the simple patterns that people can easily wrap their heads around. This would include patterns like you would see on a typical soccer ball or a pattern interior designers enjoy using where they have a regular octagons and use squares to fill in the spaces between some of the octagons. These tessellations have more than one kind of regular polygon (Coolman, 2015). When we start moving into semi-regular tessellations, we start to see some more intricate patterns immerge. This is what we typically think of when we talk about bathroom tiling or honeycomb. Some examples of this are trihedral and tetrahedral, for triangle or quadrilateral shapes ("From Mathematics", 2016). This is the simple regular polygon set in a repeating pattern, often classified by the number of sides the polygon being used has. When people think of tessellations, they commonly think about what we refer to as regular tessellations. There are varying types that we enjoy using for various purposes. However, there isn't just one type of tessellations. Some occur naturally, such as the honeycomb or animal skins. Outside the home, common examples appear in honeycomb, flower petals, reptile skin, giraffe spots, or decorative fencing (Fathauer, 2015). Some places you might be familiar with these in your everyday life would be a decorative backsplash in a kitchen or a fun tile pattern in a bathroom. Types of TessellationsĪs previously discussed, tessellations are "any repeating pattern of symmetrical and interlocking shapes" (Khaira, 2009). Sir Roger Penrose was a mathematics professor at Oxford. He originally wanted to study architecture but later transitioned into graphic design. Escher was a Dutch graphic artist who lived from 1898 to 1972. 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. Picture yourself in Northern Africa, on a tour of one of the mosques.
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