Curvature ($\kappa$) measures how fast a curve turns. At any point $P$, fitting the curve with a "best fit" circle creates the Osculating Circle.
$\kappa = \frac{|x'y'' - y'x''|}{(x'^2 + y'^2)^{3/2}}$ Radius $R = \frac{1}{\kappa}$
The circle's center is at $P + R \mathbf{N}$. High curvature means a small circle (sharp turn). Low curvature means a large circle (shallow turn). Instructions: Drag horizontally on the canvas to move the point $t$ along the curve. Observe how the radius changes.
Tangent
Normal
Osculating
Circle
Curvature ($\kappa$)
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Radius ($R$)
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