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) |

(2) |

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

(3) |

**References**

Sandefur, J. T. ``Using Self-Similarity to Find Length, Area, and Dimension.'' *Amer. Math. Monthly* **103**, 107-120, 1996.

© 1996-9

1999-05-25