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Mechanism for Drawing a Logarithmic Spiral

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a
1.15
θ
5
labels
head
This Demonstration shows a mechanism for drawing a logarithmic spiral
ρ=
θ
a
. A pivot point holds a rod with a sharp wheel at the far end. The axis of the wheel is at an angle
μ
to the rod;
μ
is chosen such that
tan(μ)=ln(a)
. As the wheel digs into the plane, it gradually pulls away from the pivot point and traces the spiral.
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