Danilo Blanuša
Encyclopedia
Danilo Blanuša was a Croatia
n mathematician, physicist, engineer and a professor
at the University of Zagreb
. He was Serb and he was born in Austro-Ugarska monarchy (today Croatia).
Blanuša was born in Osijek
and attended elementary school in Vienna
and Steyer
in Austria
and gymnasium
in Osijek and Zagreb
. He studied engineering in both Zagreb and Vienna and also mathematics
and physics
. His career started in Zagreb, where he started to work and lecture. 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.
in 1946 (the Petersen graph
was the first), triggering a new area of graph theory
. 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
is equivalent to the statement that no snark is planar
. Snarks were so named later by the American mathematician Martin Gardner
in 1976, after the mysterious and elusive object of Lewis Carroll
's poem The Hunting of the Snark
.
Blanuša's most important works were related to isometric
immersions of two-dimensional Lobachevsky
plane into six-dimensional Euclid
ean space and generalizations, in the theory of the special functions (Bessel function
s), in differential geometry, and in graph theory
. His results are included in the Japan
ese mathematical encyclopedia
Sugaku jiten in Tokyo
, published by Iwanami Shoten in 1962.
His Erdős number
is 6.
, published by Max Planck
in Annalen der Physik in 1908.
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 mathematics
, physics
and astronomy
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.
Croatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...
n mathematician, physicist, engineer and a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at the University of Zagreb
University of Zagreb
The University of Zagreb is the biggest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of Southeastern Europe...
. He was Serb and he was born in Austro-Ugarska monarchy (today Croatia).
Blanuša was born in Osijek
Osijek
Osijek is the fourth largest city in Croatia with a population of 83,496 in 2011. 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 county...
and attended elementary school in Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
and Steyer
Steyer
Steyer is surname of: , German actor and musician , German politician, MdL , German politician, MdL , German footballer...
in Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
and gymnasium
Gymnasium (school)
A gymnasium is a type of school providing secondary education in some parts of Europe, comparable to English grammar schools or sixth form colleges and U.S. college preparatory high schools. The word γυμνάσιον was used in Ancient Greece, meaning a locality for both physical and intellectual...
in Osijek and Zagreb
Zagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
. He studied engineering in both Zagreb and Vienna and also mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. His career started in Zagreb, where he started to work and lecture. Blanuša was the dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
of the Faculty of Electrical Engineering, Zagreb in the 1957-58 school year. He received the Ruđer Bošković prize in 1960.
Mathematics
In mathematics, Blanuša became known for discovering the second and third known snarksSnark (graph theory)
In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...
in 1946 (the Petersen graph
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 is named for Julius Petersen, who in 1898 constructed it...
was the first), triggering a new area of graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
. The study of snarks had its origin in the 1880 work of P. G. Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...
, who at that time had proved that the four color theorem
Four color theorem
In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color...
is equivalent to the statement that no snark is planar
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...
. Snarks were so named later by the American mathematician Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
in 1976, after the mysterious and elusive object of Lewis Carroll
Lewis Carroll
Charles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...
's poem The Hunting of the Snark
The Hunting of the Snark
The Hunting of the Snark is usually thought of as a nonsense poem written by Lewis Carroll in 1874, when he was 42 years old...
.
Blanuša's most important works were related to isometric
Isometric projection
Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings...
immersions of two-dimensional Lobachevsky
Nikolai Ivanovich Lobachevsky
Nikolai Ivanovich Lobachevsky was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry...
plane into six-dimensional Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
ean space and generalizations, in the theory of the special functions (Bessel function
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
s), in differential geometry, and in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
. His results are included in the Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese mathematical encyclopedia
Encyclopedia
An encyclopedia is a type of reference work, a compendium holding a summary of information from either all branches of knowledge or a particular branch of knowledge....
Sugaku jiten in Tokyo
Tokyo
, ; officially , is one of the 47 prefectures of Japan. Tokyo is the capital of Japan, the center of the Greater Tokyo Area, and the largest metropolitan area of Japan. It is the seat of the Japanese government and the Imperial Palace, and the home of the Japanese Imperial Family...
, published by Iwanami Shoten in 1962.
His Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
is 6.
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 thermodynamicsThermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, published by Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
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 mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
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.