Gustav von Escherich

Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician.

Born in Mantua, he studied mathematics and physics at the University of Vienna.

Together with Emil Weyr he founded the journal Monatshefte für Mathematik und Physik and together with Ludwig Boltzmann and Emil Müller he founded the Austrian Mathematical Society.

He used coordinates initially introduced by Christoph Gudermann (1830) for spherical geometry, which were adapted by Escherich using hyperbolic functions.

For the case of translation of points on this surface of negative curvature, Escherich gave the following transformation on page 510:[1] which is identical with the relativistic velocity addition formula by interpreting the coordinates as velocities and by using the rapidity: or with a Lorentz boost by using homogeneous coordinates: These are in fact the relations between the coordinates of Gudermann/Escherich in terms of the Beltrami–Klein model and the Weierstrass coordinates of the hyperboloid model - this relation was pointed out by Homersham Cox (1882, p. 186).