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Difference between revisions of "Flecnode"

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''on a planar curve''
 
''on a planar curve''
  
A point at which a node (or double point; cf. also [[Node|Node]]) and an inflection (cf. also [[Point of inflection|Point of inflection]]) coincide.
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A point at which a node (or double point; cf. also [[Node]]) and an inflection (cf. also [[Point of inflection]]) coincide.
  
Thus, one of the tangents at the node has intersection multiplicity at least <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f130/f130140/f1301401.png" /> with the curve at that point.
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Thus, one of the tangents at the node has intersection multiplicity at least $4$ with the curve at that point.
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.W. Bruce,  "Lines, surfaces and duality"  ''Math. Proc. Cambridge Philos. Soc.'' , '''112'''  (1992)  pp. 53–61</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  M. Tsuboko,  "On the line complex determinant of flecnode tangents of a ruled surface and its flecnodal surfaces"  ''Memoirs Ryojun Coll. Engin.'' , '''11'''  (1938)  pp. 233–238</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  J.W. Bruce,  "Lines, surfaces and duality"  ''Math. Proc. Cambridge Philos. Soc.'' , '''112'''  (1992)  pp. 53–61</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  M. Tsuboko,  "On the line complex determinant of flecnode tangents of a ruled surface and its flecnodal surfaces"  ''Memoirs Ryojun Coll. Engin.'' , '''11'''  (1938)  pp. 233–238</TD></TR>
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</table>

Latest revision as of 20:45, 28 December 2014

on a planar curve

A point at which a node (or double point; cf. also Node) and an inflection (cf. also Point of inflection) coincide.

Thus, one of the tangents at the node has intersection multiplicity at least $4$ with the curve at that point.

References

[a1] J.W. Bruce, "Lines, surfaces and duality" Math. Proc. Cambridge Philos. Soc. , 112 (1992) pp. 53–61
[a2] M. Tsuboko, "On the line complex determinant of flecnode tangents of a ruled surface and its flecnodal surfaces" Memoirs Ryojun Coll. Engin. , 11 (1938) pp. 233–238
How to Cite This Entry:
Flecnode. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Flecnode&oldid=18929
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article