Polygonal Spiral

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 ofthis 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.

• Fundamental Lemma of Calculus of Variations
• Fundamental System
• Fundamental Theorem of Algebra
• Fundamental Theorem of Arithmetic
• Fundamental Theorem of Curves
• Fundamental Theorem of Directly Similar Figures
• Fundamental Theorem of Gaussian Quadrature
• Fundamental Theorem of Genera
• Fundamental Theorem of Plane Curves
• Fundamental Theorem of Projective Geometry
• Fundamental Theorem of Space Curves
• Fundamental Theorem of Symmetric Functions
• Fundamental Theorems of Calculus
• Fundamental Unit
• Funnel
• Fuss's Problem
• Futile Game
• Fuzzy Logic
• FWHM
• Gabriel's Horn
• Gabriel's Staircase
• Gadget
• Gale-Ryser Theorem
• Galilean Transformation
• Gallows