Definition of Tessellations
  • In geometry, to tessellate means to manipulate a finite set of shapes to cover an entire plane with no "holes", or uncovered spaces.
  • The Webster's Dictionary definition says, to lay out in a mosaic pattern of small square blocks.
  • The word tessellation is derived from a latin word that means "small stones", and "to pave with small stones".


 Unlike Webster's definition, we find that a tessellation is not limited to the shape of a square. There are other shapes that can tessellate an entire area with no extra spaces. In fact, many mathematicians would define tessellations as the tiling of polygons that do not overlap, or contain holes between shapes.

 

M.C. Escher

 

•  Escher can be regarded as the 'Father' of modern tessellations.
•  At 68, he stated, "Filling the plane has become a real mania to which I have become addicted and from which I sometimes find it hard to tear myself away."

Day & Night 1938 Poster

Sky & Water 1938 Poster

 

Tessellations Made by the Elementary Computer Classes

Everyday Examples of Tessellations