Unusual objects - pseudosphere

[phyllo]

Pseudosphere
[attachment=0]pseudosphere.png[/attachment]

In its general interpretation, a pseudosphere of radius R is any surface of curvature −1/R^2 (precisely, a complete, simply connected surface of that curvature), by analogy with the sphere of radius R, which is a surface of curvature 1/R^2.
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As early as 1639 Christiaan Huygens found that the volume and the surface area of the pseudosphere are finite,[3] despite the infinite extent of the shape along the axis of rotation. For a given edge radius R, the area is 4πR^2 just as it is for the sphere, while the volume is 2/3 πR^3 and therefore half that of a sphere of that radius.

en.wikipedia.org/wiki/Pseudosphere

[Abstract]

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