Worlds Out of Nothing pp 123-129 | Cite as

# Publication and Non-Reception up to 1855

## Abstract

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).

## Keywords

Constant Curvature Geodesic Segment Constant Negative Curvature Interesting Surface Spherical Trigonometry## Preview

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