How do I find the line element on a torus?

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SUMMARY

The discussion centers on finding the line element on a torus, specifically the ds² term, which is essential for understanding the metric of toroidal geometry. Richard initially struggled to find relevant information but later discovered that the resource from MathWorld provided the necessary metric details. The exchange highlights the importance of thorough research and revisiting sources for complex mathematical concepts.

PREREQUISITES
  • Understanding of differential geometry
  • Familiarity with metric tensors
  • Basic knowledge of toroidal structures
  • Experience with mathematical resources like MathWorld
NEXT STEPS
  • Research the properties of metric tensors in differential geometry
  • Study the mathematical representation of toroidal coordinates
  • Explore advanced topics in Riemannian geometry
  • Review examples of line elements in various geometries
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Mathematicians, physics students, and researchers interested in geometry, particularly those focusing on differential geometry and the study of toroidal structures.

robousy
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Hey folks,

Does anyone know how to get the line element on a torus? The [tex]ds^2[/tex] term.

I want to find the metric for toroidal geometry.

Any help appreciated!

Richard
 
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Hey Nick,

Thanks, I'd already looked there and thought it was no good for what I wanted, but a second deeper looked showed that it does have the metric shown there so thanks for tip.

:)
 

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