2. Regular Tessellation
 Page ID
 13597
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Goal: To appreciate polygons and support the idea that there are three regular polygons that be tessellated.
Terminology:

A polygon is a closed 2dimensional figure with straight sides

An ngon is a polygon with exactly n sides

A regular ngon is a polygon with exactly n sides, where all sides are of equal length and all interior angles of the polygon are equal. The sum of the interior angles of a regular ngon is 180°(n  2). It follows that each interior angle must measure 180°(n  2)/n. So:

A regular 3gon is an equilateral triangle. Each interior angle is 60°

A regular 4gon is a square. Each interior angle is 90°

A regular 5gon is a regular pentagon. Each interior angle is 108°

A regular 6gon is a regular hexagon. Each interior angle is 120°

A regular 7gon is a regular heptagon. Each interior angle is 900/7°, or approximately 128.6°

A regular 8gon is a regular octagon. Each interior angle is 135°


Activity:
Suppose I want to tape the same regular ngons together to make 2dimensional shapes. What are my options? I don’t want to bend or fold the ngons. Let’s just concentrate on the corners of these objects.
Fact: