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[F]or the hyperboloid of one sheet and the hyperbolic paraboloid the curvature is negative at every point.

— Luther P. Eisenhart A Treatise on the Differential Geometry of Curves and Surfaces (1909)

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The layman thinks that mathematics deals with facts and that thus there can possibly be no differences of opinion among mathematicians. We know that this is not the case.

When an hyperboloid of revolution of one sheet is deformed into another ruled surface, the circle of gorge becomes a Bertrand curve and the generators are parallel to the corresponding binormals of the conjugate Bertrand curve.

A Treatise on the Differential Geometry of Curves and Surfaces (1909)

In 1869 Dini solved the problem of geodesic representation of two surfaces upon one another. In 1896 Levi-Civita extended the problem to spaces of any order.

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