Infinite (1748). Taking (e, 1/e) as the vertex of rectangle of unit area, and applying again the squeeze that made it from the unit square, yields Generally n squeezes yields A. A. de Sarasa noted a similar observation of G. de Saint Vincent, that as the abscissas increased in a geometric series, the sum of the areas against the hyperbola increased in arithmetic series, and this property corresponded to the logarithm already in use to reduce multiplications to additions. Euler’s work made the natural logarithm a standard mathematical tool, and elevated mathematics to the realm of transcendental functions. The hyperbolic coordinates are formed on the original picture of G. de Saint-Vincent, which provided the quadrature of the hyperbola, and transcended the limits of algebraic functions. In 1875 Johann von Thünen published a theory of natural wages which used geometric mean of a subsistence wage and market value of the labor using the employer's capital. In special relativity the focus is on the 3-dimensional hypersurface in the future of spacetime where various velocities arrive after a given proper time. Scott Walter explains that in November 1907 Hermann Minkowski alluded to a well-known three-dimensional hyperbolic geometry while speaking to the Göttingen Mathematical Society, but not to a four-dimensional one. In tribute to Wolfgang Rindler, the author of a standard introductory university-level textbook on relativity, hyperbolic coordinates of spacetime are called Rindler coordinates. References David Betounes (2001) Differential Equations: Theory and Applications, page 254, Springer-TELOS, . Scott Walter (1999). "The non-Euclidean style of Minkowskian relativity" . Chapter 4 in: Jeremy J. Gray (ed.), The Symbolic Universe: Geometry and Physics 1890-1930, pp. 91–127. Oxford University Press. . Coordinate systems Hyperbolic geometry