LESSON 4. Finding Patterns
Scientists and mathematicians are always
looking for connections in math and science. They collect and analyze data to
see if a pattern emerges. If a mathematical model of an experiment can
be developed, it usually reveals what a scientist may have discovered.
We see tiling all the time from
brick walls to tiles on your bathroom walls. Artist and brick workers have
used tiles in design throughout humanity. However, mathematicians and
scientists have developed properties and rules to classify patterns. This
information may help understand materials especially at the microscopic level.
Tessellations
are an assemblage of regular polygons
that do not overlap and creates an arrangement or repeatable pattern.
The word “tessellate” is derived from a Greek derivation which refers to the
four corners of the tiles in a mosaic. Only three regular polygons tessellate
in the Euclidean plane: triangles, squares and hexagons. The pattern
caused by all triangles needs to “flip flop” the triangles to make them fit.
A square and a hexagon stack up without inverting one of the shapes.
Equilateral triangles have three-fold symmetry, squares have
four-fold symmetry, and hexagons have six-fold symmetry. |