Ellipse in intrinsic coordinates

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SUMMARY

The discussion centers on the mathematical representation of an ellipse in intrinsic coordinates, specifically focusing on direction and curve length. Participants seek a definitive equation for ellipses and other conic sections in this context. The links provided direct users to MathWorld resources, which include detailed explanations of ellipses and elliptic cylindrical coordinates. The inquiry highlights the complexity of deriving such equations despite their seemingly straightforward nature.

PREREQUISITES
  • Understanding of conic sections, particularly ellipses.
  • Familiarity with intrinsic coordinates in mathematics.
  • Basic knowledge of curve length calculations.
  • Access to mathematical resources such as MathWorld.
NEXT STEPS
  • Research the mathematical properties of ellipses in intrinsic coordinates.
  • Explore the derivation of curve length formulas for conic sections.
  • Study elliptic cylindrical coordinates and their applications.
  • Examine related mathematical concepts in differential geometry.
USEFUL FOR

Mathematicians, physics students, and anyone interested in advanced geometry or the mathematical modeling of curves.

chronon
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Does anyone know an equation for an ellipse (or other conics) in intrinsic coordinates, that is direction and curve length. It's the sort of thing that looks like it should be simple, but I've a feeling it may in fact be somewhat messy.
 
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