Vladimir Varićak

Vladimir Varićak (sometimes also spelled Vladimir Varičak; March 1, 1865, Otočac – January 17, 1942, Zagreb) was a Croatian mathematician and theoretical physicist.

Varićak, an ethnic Serb, was born in the village of Švica near Otočac, Austrian Empire (present-day Croatia). He studied physics and mathematics at the University of Zagreb from 1883 to 1887. He made his PhD in 1889 and got his habilitation in 1895. In 1899 he became professor of mathematics in Zagreb, where he gave lectures until his death in 1942.

From 1903 to 1908 he wrote on hyperbolic geometry (or Bolyai–Lobachevskian geometry). In 1910, following a 1909 publication of Sommerfeld, he applied hyperbolic geometry to the special theory of relativity. Sommerfeld, using the imaginary form of Minkowski space, had shown in his 1909 paper that the Einstein formula for combination of velocities is most clearly understandable as a formula for triangular addition on the surface of a sphere of imaginary radius. Varićak reinterpreted this result as showing that rapidity combines by the triangle rule in hyperbolic space. This is a fundamental result for the hyperbolic theory which was demonstrated later by other approaches by Robb (1911) and Borel (1913). The 1910 papers also dealt with several applications of the hyperbolic theory to optics. In 1911 Varićak was invited to speak to the Deutsche Mathematiker-Vereinigung in Karlsruhe on his work. He continued to develop the hyperbolic reinterpretation of Einstein's theory collecting his results in 1924 in a textbook, Darstellung der Relativitätstheorie im drei-dimensionalen Lobatschefskijschen Raume (Relativity in Three-Dimensional Lobachevski Space), now available in English. In the period 1909 to 1913 Varićak had correspondence with Albert Einstein concerning rotation and length contraction where Varićak's interpretations differed from those of Einstein. Concerning length contraction Varićak said that in Einstein's interpretation the contraction is only an "apparent" or a "psychological" phenomenon due to the convention of clock measurements whereas in the Lorentz theory it was an objective phenomenon.

...
Wikipedia