Publication and Non-Reception up to 1855

Part of the Springer Undergraduate Mathematics Series book series (SUMS)


An interesting surface was discussed by H. F. Minding in the 1830s in papers he published in Crelle’s Journal [159] although these papers were then largely forgotten for 30 years; this was a surface of constant negative curvature with the property that geodesics between points are not necessarily unique. Minding’s surface is formed by rotating a tractrix about its vertical axis. A tractrix — the name is due to Huyghens — is the curve of the obstinate dog. A point Q on a line ℓ is attached to a point P by a curve of fixed length. P, the dog, is dragged behind Q, the owner, who walks along ℓ, and the path of P is called the tractrix. It is conventional for the walk to start with PQ perpendicular to ℓ. Minding’s surface, which is sometimes called the pseudosphere, is formed by rotating the tractrix about ℓ; the point P then generates a circle of singular points (see Figure 11.1).


Constant Curvature Geodesic Segment Constant Negative Curvature Interesting Surface Spherical Trigonometry 
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© Springer-Verlag London Limited 2007

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