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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.

— Luther P. Eisenhart

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More quotes by Luther P. Eisenhart

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

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

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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Quote text and notes from Wikiquote: Luther P. Eisenhart (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.