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6. Curvature and Osculating Circles

In three-space, the evolute to a curve X(t) is defined as the following curve:

    E(t) =X(t) +[1/k(t)]P(t)
Circles in the osculating plane , centered along the evolute with a radius of 1k(t) are known as osculating circles just as in the planar case. Locally in the osculating plane, the curve passes just inside of the circle on one side of the point of contact and just outside on the other.

Demonstration 9: Osculating Circles in 3-space Demo
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The default function is an exponential spiral. The tapedeck can be used to move a single osculating circle around the curve.

This demo displays a curve with some of its osculating circles.


Next: Parallel Curves