regular smooth curve - Penn Math
regular smooth curve - Penn Math
regular smooth curve - Penn Math
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THEOREM. Given <strong>smooth</strong> functions �(s) > 0<br />
and �(s) , for s � I , there exists a <strong>regular</strong> <strong>curve</strong><br />
�: I � R 3 parametrized by arc length,<br />
with curvature �(s) and torsion �(s) .<br />
Moreover, another other such <strong>curve</strong> �: I � R 3<br />
differs from � by a rigid motion of R 3 .<br />
This result is sometimes called the<br />
fundamental theorem of the local theory of <strong>curve</strong>s.<br />
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