WOLFRAM|DEMONSTRATIONS PROJECT

Drawing a Logarithmic Spiral

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a
1.1
1.2
1.3
1.4
1.6
n
12
16
24
draw!
show labels for A, B, C
This Demonstration shows an approximation of the logarithmic spiral
ρ=
θ
a
. Draw
n
equally spaced rays from the origin
O
. The point
A
is on the polar axis at a distance 1 from the origin. The point
B
is on the ray
2π/n
at the distance
b=
2π/n
a
. So
A
and
B
are on the spiral. Draw a point
C
so that the triangles
OAB
and
OBC
are similar. From
OA:OB=OB:OC
, we get
OC=
2
b
. On the ray
4π/n
, draw a point at distance
OC
; this point will be on the spiral. Continue in this way. Note that 1,
b
,
2
b
, … form a geometric sequence.