Pathological curves. Angular points

mercoledì, Dicembre 2nd, 2020

exercises in differential geometry,pathological curves,sngular points

We conclude this brief review of differential geometry exercises to show the following: any parametric representation x = x (t), y = y (t) of a plane curve, with x (t), y (t) functions of class C ^ oo, does not imply the regularity of the curve. In other words, the continuity of functions and derivatives of any high order, is a necessary but not sufficient condition for regularity.
The proposed exercise shows a curve with an corner point .

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