# Drawing a Logarithmic Spiral

Drawing a Logarithmic Spiral

This Demonstration shows an approximation of the logarithmic spiral . Draw equally spaced rays from the origin . The point is on the polar axis at a distance 1 from the origin. The point is on the ray at the distance . So and are on the spiral. Draw a point so that the triangles and are similar. From , we get . On the ray , draw a point at distance ; this point will be on the spiral. Continue in this way. Note that 1, , , … form a geometric sequence.

ρ=

θ

a

n

O

A

B

2π/n

b=

2π/n

a

A

B

C

OAB

OBC

OA:OB=OB:OC

OC=

2

b

4π/n

OC

b

2

b