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)
|
The total length of the spiral for an 
-gon with side length 
is therefore
 |  |  |
(2)
|
 |  | ![s/(2[1-cos(pi/n)]).](/images/equations/PolygonalSpiral/Inline9.svg) |
(3)
|
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)
|
The shaded triangular polygonal spiral is a rep-4-tile.
