Arclets

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
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Arclets printable sheet



Each of the following arclets is made from arcs of a circle of radius r.

         

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Arclets
 

What is the perimeter of an arclet with 3, 4, 5, and n "nodes"?

What happens when n is very large?

Explain the relationship between your answers and the perimeter of the original circle.