##  [Cusp Singularity](/cusp-singularity) 

  ##  [Cusp Singularity](https://mathlogic.quantumdictionary.io/cusp-singularity-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A localized non-smooth point on a curve or surface where the tangent (or tangent plane) degenerates so that the local geometry has a pointed, sharp form; analytically, it is a singular point at which derivatives fail to define a regular tangent direction, for example the plane cusp parametrized by t ↦ (t^2,t^3).