Geodesic
Extended Hyperbolic Surfaces in~$R^3$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 267-279

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In this paper, I will describe the construction of several surfaces whose intrinsic geometry is hyperbolic geometry, in the same sense that spherical geometry is the geometry of the standard sphere in Euclidean 3-space. I will prove that the intrinsic geometry of these surfaces is, in fact, (a close approximation of) hyperbolic geometry. I will share how I (and others) have used these surfaces to increase our own (and our students') experiential understanding of hyperbolic geometry. (How to find hyperbolic geodesics? What are horocycles? Does a hyperbolic plane have a radius? Where does the area formula $\pi r^2$ fit in hyperbolic geometry?). 
@article{TM_2004_247_a19,
     author = {D. W. Henderson},
     title = {Extended {Hyperbolic} {Surfaces} in~$R^3$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {267--279},
     publisher = {mathdoc},
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     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_247_a19/}
}
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D. W. Henderson. Extended Hyperbolic Surfaces in~$R^3$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 267-279. http://geodesic.mathdoc.fr/item/TM_2004_247_a19/