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Difference between revisions of "Breaking point"

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''angle point''
 
''angle point''
  
A singular point of a plane curve with the property that two branches of the curve end in it in such a way that each has a (one-sided) tangent at the point different from the other. For example, the origin is a breaking point of the curve <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b017/b017630/b0176301.png" /> (see Fig.). The left and right derivatives are different at a breaking point.
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A singular point of a plane curve with the property that two branches of the curve end in it in such a way that each has a (one-sided) tangent at the point different from the other. For example, the origin is a breaking point of the curve $y=x/(1+e^{1/x})$ (see Fig.). The left and right derivatives are different at a breaking point.
  
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/b017630a.gif" />
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/b017630a.gif" />
  
 
Figure: b017630a
 
Figure: b017630a

Revision as of 21:50, 30 April 2014

angle point

A singular point of a plane curve with the property that two branches of the curve end in it in such a way that each has a (one-sided) tangent at the point different from the other. For example, the origin is a breaking point of the curve $y=x/(1+e^{1/x})$ (see Fig.). The left and right derivatives are different at a breaking point.

Figure: b017630a

How to Cite This Entry:
Breaking point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Breaking_point&oldid=32016
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article