The Shape of Space: Tilings
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 Angela M
"This spooky library scene is a fantastic instance of monohedral tiling.
These parallelograms/diamonds are all the same shape & size, and
each four sided, regular polygon coincides entirely with the edge of a
bordering tile, as this is also an example of edge-to-edge tiling.
(Vertex type: 4.4.4.4.) "
comment By Emerald_b
Credit To Angela.M
"this is probably the most common tiling we can see in our daily life. Triangle and octagon tiling the whole plane without any blank (8,4,8,4)"
Comment By Chaoran Zhang
Comment By Lily.A
