section_path: Main concepts/Measures: length, area, and volume/Metrics and measures
section_name: Metrics and measures
paragraph_text: Metrics and measures
  
  The concept of length or distance can be generalized, leading to the idea of metrics. For instance, the Euclidean metric measures the distance between points in the Euclidean plane, while the hyperbolic metric measures the distance in the hyperbolic plane. Other important examples of metrics include the Lorentz metric of special relativity and the semi- Riemannian metrics of general relativity.
  
  In a different direction, the concepts of length, area and volume are extended by measure theory, which studies methods of assigning a size or measure to sets, where the measures follow rules similar to those of classical area and volume.