Suffice to say, many other types of tessellation are possible under different sets of rules. Escher, 1936.īeing the farthest thing from a mathematician or scientist, from this point on tessellation go way over my head. Fyodorov was the first to engage in a mathematical study of tessellations.Īn Alhambra tessellation as drawn by M.C. About two-hundred years later, in 1891, the Russian scientist, Yevgraf Fyodorov, in studying the arrangement of atoms in the crystalline solids, proved that every periodic tiling features one of seventeen different groups of isometries (reflections, rotations, and translations). He was the first to explore and explain the hexagonal structures of honeycombs and snowflakes. He wrote about regular and semi-regular tessellations in his Harmonices Mundi. In 1619 the German mathematician, Johannes Kepler, made one of the earliest documented study of tessellations. Since that time, they've been an element in virtually every civilization having developed an advanced decorative culture. They go back some five-thousand years to the Sumerian culture (above) of around 3300-3000 BC (located in modern-day Iraq). Tessellations are not the artistic stepchild of modern-day mathematics. Notice the faint vertical and diagonal guidelines used to align the tiles.Ĭone mosaic pattern columns, ca. Each tile may contain non-tessellating decorative elements as well. Tessellations tiles need not have straight edges. If the right contrasting colors are chosen for the tiles of the various shapes, amazing patterns are formed, and these can be used to decorate physical surfaces. Escher, famous for making tessellations with irregular interlocking tiles, shaped like animals and other natural objects (above).
Undoubtedly the most famous artist to utilize tessellations was M.C. Mathematics being a rigidly left-brain subject, it would be fair to say this was an example of left-brain art.an art form ruled by rules. I don't recall for sure, but I think these were probably plane geometry students, which is not exactly higher mathematics but neither is it a playground for imbeciles. Students were coming up with incredibly complex designs (similar to the one above), some just short of mind-boggling. I kept my mouth shut and observed (a tactic I'd advise for anyone knowing little or nothing about any subject). Yet students were coming to me for help in making theirs.
#MATH TESSELLATION ART HOW TO#
I'm ashamed to say it now, but at the time, I had never even heard of such things, much less how to create one.
They were having students create tessellations. Many, many years ago, when I first became a high school art instructor, I was somewhat startled to find that our high school math department also taught art.
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