The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of sides is
(1)
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The total length of the spiral for an -gon with side length is therefore
(2)
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(3)
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Consider the solid region obtained by filling in subsequent triangles which the spiral encloses. The area of this region, illustrated above for -gons of side length , is
(4)
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The shaded triangular polygonal spiral is a rep-4-tile.