What is the Hyperbola of Apollonius?

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SUMMARY

The discussion clarifies that the term "hyperbola of Apollonius" specifically refers to rectangular hyperbolas. Apollonius of Perga is credited with naming conic sections, including hyperbolas, which are defined through the intersection of a plane and a cone. The term "hyperbola of Apollonius" lacks standalone meaning without context, as it pertains to a specific point in relation to a conic. Reference to theorem 26 in a specific mathematical text further supports this definition.

PREREQUISITES
  • Understanding of conic sections, specifically hyperbolas
  • Familiarity with Apollonius of Perga's contributions to geometry
  • Knowledge of the relationship between conics and oblique cones
  • Access to mathematical literature discussing theorems related to hyperbolas
NEXT STEPS
  • Study the properties of rectangular hyperbolas in detail
  • Review Apollonius's work on conic sections
  • Examine theorem 26 in the referenced mathematical text for deeper insights
  • Explore the applications of hyperbolas in modern geometry and physics
USEFUL FOR

Mathematicians, geometry enthusiasts, and students studying conic sections will benefit from this discussion, particularly those interested in the historical context and definitions of hyperbolas.

ralphiep
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Simple question. Is what we now call a 'rectangular hyperbola' what was once called the hyperbola of Apollonius? Thanks
 
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Hi ralphiep. :smile:

As far as I know Apollonius was the one who named the conics, i.e parabola, ellipse, and hyperbola. He related them to the well known analogy of slicing an oblique cone. That obviously includes the regular(non rectangular) hyperbolas.
 

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