Our ancestors had an artistic impulse to cover floors and walls with patterns and mosaics, in buildings ranging from Roman dwellings to Muslim mosques. They expressed the same desire for patterns in other decorative arts as well—carpets, fabrics, baskets, and even linoleum.
They use repeated shapes (“tiles”) to cover a flat surface, without gaps or overlaps. Such patterns,apart from their esthetic appeals, can also have practical applications. In manufacturing, for example, stamping components from a sheet of metal is most economical if the shapes of the components fit together without gaps—in other words, if the shapes form a tiling.
Definition:
A tiling (tessellation) is a covering of the entire infinite plane by non overlapping regions called tiles.
We have some great examples from our class
Credit To Lily A
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| http://math125fall2014.blogspot.com/2014/09/tiling-in-nature.html#comment-form |
"The tiling's fundamental domain is a hexagon. it's vertex type is the point where three hexagons meet. the internal angle of a hexagon is 120 degrees. when you add the three internal angles at the vertex type you get 360 degrees."
Comment By Sophia Darby
Credit To Schuyler E
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| http://math125fall2014.blogspot.com/2014/09/tiling_44.html#comment-form |
"This image is an example of monohedral tiling with regular polygons (hexagons)"
Comment By Angela M
Credit To Paige B
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| http://math125fall2014.blogspot.com/2014/09/tiling_22.html#comment-form |
"This is a semiregular tiling with a fundamental domain of one square and one (slightly) irregular octagon. Each vertex is an 8, 8, 3 type. Therefore, the exterior angles at each vertex measure 45, 45, and 90 degrees respectively."
Comment By Lily A
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