Danilo Blanuša (7 December 1903 – 8 August 1987) was a

Croatia Croatia, officially the Republic of Croatia, is a country in Central Europe, Central and Southeast Europe, on the coast of the Adriatic Sea. It borders Slovenia to the northwest, Hungary to the northeast, Serbia to the east, Bosnia and Herze ...

n mathematician, physicist, engineer and a

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

at the

University of Zagreb The University of Zagreb (, ) is a public university, public research university in Zagreb, Croatia. It is the largest Croatian university and one of the oldest continuously operating universities in Europe. The University of Zagreb and the Unive ...

Biography

Blanuša was born in

Osijek Osijek () is the fourth-largest city in Croatia, with a population of 96,848 in 2021. It is the largest city and the economic and cultural centre of the eastern Croatian region of Slavonia, as well as the administrative centre of Osijek-Baranja ...

Austria-Hungary Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe#Before World War I, Central Europe between 1867 and 1918. A military ...

(today

). He attended elementary school in

Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...

and

Steyr Steyr (; ) is a statutory city (Austria), statutory city, located in the Austrian federal state of Upper Austria. It is the administrative capital, though not part of Steyr-Land District. Steyr is Austria's 12th most populated town and the 3rd lar ...

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

and gymnasium in Osijek and

Zagreb Zagreb ( ) is the capital (political), capital and List of cities and towns in Croatia#List of cities and towns, largest city of Croatia. It is in the Northern Croatia, north of the country, along the Sava river, at the southern slopes of the ...

. He studied engineering in both Zagreb and Vienna and also

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

. His career started in Zagreb, where he started to work and lecture. His student Mileva Prvanović completed her doctorate in 1955, the first in geometry in

Serbia , image_flag = Flag of Serbia.svg , national_motto = , image_coat = Coat of arms of Serbia.svg , national_anthem = () , image_map = , map_caption = Location of Serbia (gree ...

. Blanuša was the dean of the Faculty of Electrical Engineering, Zagreb in the 1957–58 school year. He received the Ruđer Bošković prize in 1960. He died in

Mathematics

In mathematics, Blanuša became known for discovering the second and third known snarks in 1946 (the

Petersen graph In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph i ...

was the first), triggering a new area of

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. The study of snarks had its origin in the 1880 work of P. G. Tait, who at that time had proved that the

four color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions shar ...

is equivalent to the statement that no snark is planar. Snarks were so named later by the American mathematician

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

in 1976, after the mysterious and elusive object of

Lewis Carroll Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglicanism, Anglican deacon. His most notable works are ''Alice ...

's poem ''

The Hunting of the Snark ''The Hunting of the Snark'', subtitled ''An Agony, in Eight Fits'', is a poem by the English writer Lewis Carroll. It is typically categorised as a nonsense poem. Written between 1874 and 1876, it borrows the setting, some creatures, and eig ...

''. Blanuša's most important works were related to isometric immersions of

pseudo-Riemannian manifold In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the ...

s in

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. In particular, in his most cited work he has exhibited an embedding of a hyperbolic ( Lobachevsky) two-dimensional plane into 6-dimensional

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ...

and another construction, for all natural numbers

n\geq 2

, of an

n

-dimensional hyperbolic space into

6n-5

-dimensional Euclidean space. In an earlier work D. Blanuša, Eine isometrische und singularitätenfreie Einbettung des

n

-dimensionalen hyperbolischen Raumes im Hilbertschen Raum. Monatsh. f. Math. 57 (1953) 102–108. he has exhibited embeddings of

n

-dimensional hyperbolic spaces into a separated (infinite-dimensional) Hilbert space. His other important works are in the theory of the special functions (

Bessel function Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...

s) and in

. Some of his results are included in the

Japan Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...

ese mathematical

encyclopedia An encyclopedia is a reference work or compendium providing summaries of knowledge, either general or special, in a particular field or discipline. Encyclopedias are divided into article (publishing), articles or entries that are arranged Alp ...

''Sugaku jiten'' in

Tokyo Tokyo, officially the Tokyo Metropolis, is the capital of Japan, capital and List of cities in Japan, most populous city in Japan. With a population of over 14 million in the city proper in 2023, it is List of largest cities, one of the most ...

, published by ''Iwanami Shoten'' in 1962.

Physics

His works were mostly related to the theory of relativity. He discovered a mistake in relations for absolute heat Q and temperature T in relativistic phenomenological

thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, published by

Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...

in ''Annalen der Physik'' in 1908. * Q0 and T0 are the corresponding classical values, and a=(1-v₂/c₂)^1/2 in the relation → Q=Q0a, T=T0a really should be → Q=Q0/a, T=T0/a This correction was published in '' Glasnik'', the journal relating to

and

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

in 1947 in the article "Sur les paradoxes de la notion d'énergie". It was rediscovered in 1960, and the correction is still wrongly attributed to H. Ott in the mainstream scientific literature.

References

External links

Blanuša snarks in the logo of the Croatian Mathematical Society

Blanuša snark on a Croatian postage stamp

{{DEFAULTSORT:Blanusa, Danilo 20th-century Croatian mathematicians Yugoslav mathematicians Yugoslav engineers Croatian mathematicians Members of the Croatian Academy of Sciences and Arts Academic staff of the University of Zagreb Faculty of Science, University of Zagreb alumni People from Osijek Serbs of Croatia Burials at Mirogoj Cemetery 1903 births 1987 deaths

Biography

Mathematics

Physics

See also

References

External links