How do tessellations work

1. Tessellations
By Joe Belnap

2. Overview
According to Math 4 Kids- Basically,
a tessellation is a way to tile a floor
(that goes on forever) with shapes
so that there is no overlapping and
no gaps.
http://www.coolmath4kids.com/tesspag1.html
http://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Wallpaper_group-p3-1.jpg/300px-Wallpaper_group-p3-1.jpg

3. M.C. ESCHER
M.C. Escher used
tessellations in his art.
http://3.bp.blogspot.com/_GjYTzeJ9A_Y/SidaI7Fa6UI/AAAAAAAAABc/wx-eSRkKzHk/s400/tess.liz.jpg
http://mrcoley.com/art/images/escher03.jpg
http://britton.disted.camosun.bc.ca/escher/pegasus.jpg

4. Tessellations in Nature
Many regular tessellations can
be found in nature: Beehive,
pineapple, snake skin, etc.
http://androidos.in/wp-content/uploads/2011/01/honeycomb.jpg

5. Regular Tessellations
A regular tessellation is a regular
polygon that can tile a flat surface
using the same type of polygon. There
are only three regular tessellations.

6. Semi-Regular Tessellations
Semi regular tessellations are a mix of
two or more regular polygons to fill a flat
plane with no gaps or open spaces. There
are eight semi-regular tessellations that
tessellate.

7. Why do only certain shapes
tessellate?
Each polygon that can tessellate has
an interior angle that can be added
with any other polygons’ interior
angles. For example, the interior
angle of an equilateral
triangle is 60o. The
interior angle of a
3-3-3-
4-4 quadrilateral is 90o. When
a point is picked in this
tessellation the
surrounding angles all add up to 360o.