##  [Isometry](/isometry) 

  ##  [Isometry](https://natural.quantumdictionary.io/isometry-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A map between metric spaces that preserves distances exactly: for all points x and y, the distance between f(x) and f(y) equals the distance between x and y.

 

 

 

 

 





 

 



 ##  [Isometry](https://puremath.quantumdictionary.io/isometry-1) 

  

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

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A map between metric spaces that preserves distances exactly: for all x,y, d(f(x),f(y)) = d(x,y). In Euclidean spaces isometries are geometry-preserving transformations such as translations, rotations, and reflections.