In the interactive figure, drag point [i]P[/i] along the curve from point [i]A[/i] to point [i]B[/i]. The principal unit normal vector [math]\mathbf{N}[/math] is always perpendicular to the unit tangent vector [math]\mathbf{T}[/math], and always points towards the center of curvature [i]C[/i]. The circle centered at [i]C[/i] and passing through point [i]P[/i] shares the same tangent line to the curve at point [i]P[/i]. [br][br]Drag points [i]A[/i] and [i]B[/i], as well as the three control points on the curve to explore different paths.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]