Danilo Blanusa
Danilo Blanusa (1903-1987), Croatian mathematician, professor at the University of Zagreb, was born in Osijek. He discovered a mistake in relations for absolute heat Q and temperature T in relativistic phenomenological thermodynamics, published by Max Planck in Annalen der Physik in 1908: Q = Q0 a, T = T0 a , where Q0 and T0 are the corresponding classical values, and a = (1-v2/c2)1/2. Blanusa proved that the correct relations should be Q = Q0 / a, T = T0 / a . This result that he published in Glasnik mat.-fiz i astr., 2/1947 (No 4-5), pp 249-250, in his article “Sur les paradoxes de la notion d’énergie” [PDF], was rediscovered 13 years later by Heinrich Ott, and published in “Zeitschrift für Physik” in 1963. It is already time to correct wrong attribution of this discovery to Heinrich Ott in the scientific literature, since Blanusa’s priority is indisputable. Blanusa’s most important work is related to isometric immersions of two-dimensional Lobacevski plane into six-dimensional Euclidean space and generalizations. This result is included in authoritative Japanese mathematical encyclopedia Sugaku jiten published by Iwanami shoten, Tokyo, 1962, p. 612. His work about imbeddings of hyperbolic spaces into Euclidean spaces has been cited in 1956 by John Nash (well known mathematician, Nobel prize for economy; Blanusa is cited in his paper “The imbedding problem for Riemannian manifolds”, Annals of Mathematics, Vol 63, No. 1, 1956, pp. 20-63).
His work in graph theory resulted with what is now known as
- Blanusa’s Snark
- Blanusa’s Snark at Wolfram Research
- Tomislav Petkovic: D. Blanusa’s formulae for heat and temperature transformations in relativistic thermodynamics and his correspondence with W. Pauli in 1948, [PPT]
- photos
It is not widely known that Max Planck visited the Croatian capital Zagreb in the automn 1942, when he was at the age of 84. He delivered a lecture at the University of Zagreb on September 15th, entitled “On the goals and boundaries of exact natural sciences” (sources: Priroda, Zagreb 1942, p 184, or Glasnik Mat. Fiz. Astr. 2, 1947, p 213). Max Planck spent a few days in Zagreb lodged at the appartment of academician Stjepan Ivisic, distinguished Croatian linguist and polyglot. (Many thanks to Mrs. Ljiljana Ivsic, granddaughter of Stjepan Ivisic,for this information, 2015 ; also according to her information, the family of Ivsic is in possession of a personal letter of Max Planck addressed to Stjepan Ivsic.)