##  [Tacnode](/index.php/tacnode) 

  ##  [Tacnode](https://puremath.quantumdictionary.io/tacnode-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A plane curve singularity where two distinct smooth branches meet with higher-order tangency (osculation), so that they share the same tangent direction and meet with intersection multiplicity greater than two; a standard local model is y^2 = x^4 or two branches with contact of order two.

 

 

 

 

 





 

 



 ##  [Tacnode](https://algebra.quantumdictionary.io/tacnode-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A tacnode is a planar singularity where two smooth branches have a common tangent and osculate to higher order at their contact point; geometrically the branches meet with higher-order tangency rather than transversely.