regular smooth curve - Penn Math
regular smooth curve - Penn Math
regular smooth curve - Penn Math
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Problem 18. (a) Show that the total curvature of a <strong>regular</strong><br />
closed <strong>curve</strong> in the plane is 2n� for some integer n .<br />
(b) Show that if the <strong>regular</strong> closed <strong>curve</strong> is simple,<br />
then n = +1 or —1 .<br />
(c) Suppose that a <strong>regular</strong> closed <strong>curve</strong> in the plane has<br />
curvature which is strictly positive or strictly negative,<br />
and that the above integer n equals +1 or —1 .<br />
Show that the <strong>curve</strong> is simple.<br />
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