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Prove. The normal N to surface S at point (r, s) — which corresponds to point P on C — is parallel to the binormal B of curve C at P.

Proof. The equation of the tangent surface S of curve C is given by


The normal to S at point (r, s) is given by ole1.gif so we now compute it. Taking derivatives of 1) we get



where ole4.gif is the principal normal to curve C at point P. Thus


Since ole6.gif and ole7.gif we have


where ole9.gif is the binormal to C at P. Thus the normal ole10.gif is a multiple of ole11.gif

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