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...Differential geometry line integrals notation formulas review let c be an oriented curve parameterized by r t hx y z i where a b denotes the with its orientation e direction reversed we denote and joined together such curves don have to connected more generally is travel along backwards times then run total of dene s u du this arc length function note dt second part ds fundamental theorem calculus so that element used in denition respect unit tangent n normal binormal for every these are dened they mutually perpendicular vectors tnb frame forms right handed system much like variable ijk triple particular andb wecanthinkoftaspointing forward pointing left up just decomposing vector into j k components can decomposed curvature given rst formula shows depends only on shape not parameterization easy use when has already been computed third easiest apply if computing from scratch measures how bent circle radius larger circles less also all or segment even many dierentiable may exist at leas...