Tacnode
From Encyclopedia of Mathematics
point of osculation, osculation point, double cusp
The third in the series of 
-curve singularities. The point 
is a tacnode of the curve 
in 
.
The first of the 
-curve singularities are: an ordinary double point, also called a node or crunode; the cusp, or spinode; the tacnode; and the ramphoid cusp.
They are exemplified by the curves 
for 
.
The terms "crunode" and "spinode" are seldom used nowadays (2000).
References
| [a1] | A. Dimca, "Topics on real and complex singularities" , Vieweg (1987) pp. 175 |
| [a2] | R.J. Walker, "Algebraic curves" , Princeton Univ. Press (1950) (Reprint: Dover 1962) |
| [a3] | Ph. Griffiths, J. Harris, "Principles of algebraic geometry" , Wiley (1978) pp. 293; 507 |
| [a4] | S.S. Abhyankar, "Algebraic geometry for scientists and engineers" , Amer. Math. Soc. (1990) pp. 3; 60 |
How to Cite This Entry:
Tacnode. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tacnode&oldid=23988
Tacnode. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tacnode&oldid=23988
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article