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Hyperbolic Geometry

In: Geometric Algebra with Applications in Science and Engineering

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  • Hongbo Li

Abstract

Hyperbolic geometry is an important branch of mathematics and physics. For hyperbolic n-space, there are five important analytic models: the Poincaré ball model, the Poinca re half-space model, the Klein ball model, the hemisphere model and the hyperboloid model. The hyperboloid model is defined to be one branch H n of the set $$ \left\{ {x{ \in ^{{n,1}}}|x \cdot x = - 1} \right\}. $$

Suggested Citation

  • Hongbo Li, 2001. "Hyperbolic Geometry," Springer Books, in: Eduardo Bayro Corrochano & Garret Sobczyk (ed.), Geometric Algebra with Applications in Science and Engineering, chapter 0, pages 61-85, Springer.
  • Handle: RePEc:spr:sprchp:978-1-4612-0159-5_4
    DOI: 10.1007/978-1-4612-0159-5_4
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