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Tessellations
7/30/2009
Title slide
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Definition
A tessellation is a filling up of a 2-dimensional space with the same
shape without any overlap or spaces.
A tessellation of hexagons
A tessellation of triangles.
A tessellation of trapezoids
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Empty spaces, overlap
Tessellations cannot have any empty spaces or overlap.
Overlap
Open
spaces
Pentagons do not tessellate.
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Tessellations
7/30/2009
Sum of corner angles is 360º
Shapes that tessellate join at the vertices to add up 360⁰
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Fraction of 360º
Shapes that don’t tessellate have a fractional part missing
from 360⁰
Does not fill
the circle or
360º.
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Mathematical Concepts
The measures of the angles that meet at
the corners must add up to exactly 360º.
The sum of all the angles in a polygon
= ( n - 2 )·180º,
where n is the number of sides.
The measure of one angle is the sum of
the angles divided by n.
For equal numbers to add up to 360º they
must go into 360º evenly.
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Tessellations
7/30/2009
Ex. 1 Does an octagon tessellate?
 Find the sum of the measures of all the interior angles.
Sum m’s = 180 (n-2)
=180 (8-2)
=180 (6)
Sum m’s =1080º
 Find the measure of one angle.
m = 1080  8
space
m = 135º
 Divide 360 ⁰ by 135º.
Ratio = 360/135= 2.67
Conclusion: An octagon does not tessellate because
the ratio of 360 to 135 is not a whole number.
overlap
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Ex. 2 Does a hexagon tessellate?
 Find the sum of the measures of all the interior angles.
Sum m’s = 180 (n-2)
=180 (6-2)
=180 (4)
Sum m’s =720º
 Find the measure of one angle.
m = 720 6
m = 120º
 Divide 360 ⁰ by 120º.
Ratio = 360/120= 3
Conclusion: An octagon does tessellate because
120 goes evenly into 360.
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Websites of Interest
Checked on 7/11/09
Math Forum: Tessellation Tutorials by Suzanne Alejandre
Shodor Interactivate: Tessellate!
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