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n.1.(Geom.) The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.
Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
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One can isometrically embed the portion 0 < [absolute value of (u)] < 1/e of the hyperbolic punctured disk into Euclidean [R.sup.3] as the open half tractricoid (the surface obtained by revolving an open half of a tractrix along its asymptote [20]) E defined in cylindrical coordinates (r,[theta],[x.sub.3]) (where [x.sub.1] = r cos [theta] and [x.sub.2] = r sin [theta]) by the parametric equations:
Caption: Figure 3: Upper half of a tractricoid (pseudosphere).