# Theodor Angheluță

### Quick Info

Born
28 April 1882
Died
30 May 1964
Cluj, Romania

Summary
Theodor Angheluță was a Romanian mathematician who made important contributions to Function Theory, to Differential and Integral Equations, and to Functional and Algebraic Equations.

### Biography

Theodor Angheluță was born in April 1882 in the small village Adam situated in the (former) Tutova county. Tutova County was one of the historic counties of Moldavia and is now part of Galati county in Romania. He was born into a peasant family.

After the primary and secondary studies at Bârlad, a major city about 30 km north of the village of Adam where he was born, he became a student in the Faculty of Sciences at the University of Bucharest in 1902. He was awarded his bachelor's degree in Mathematics in 1905. After graduating, he became a secondary school teacher of mathematics. He was a school teacher from 1905 to 1909. From 1910, Theodor Angheluță was a student at the Sorbonne in Paris, working mainly on the guidance of Émile Picard. He had to return to Romania in 1914 because of the outbreak of World War I, but he spent the next few years, from 1914 to 1919, as a secondary school mathematics teacher. Theodor Angheluță was appointed associate professor in the Faculty of Sciences of the University of Bucharest in 1919. On 16 June 1922 Angheluță defended his Ph.D. thesis On a general class of trigonometric polynomials and the approximation of a continuous function at the University of Bucharest.

After the award of his doctorate, in 1923 Angheluță was appointed as a full professor of Algebra in the Faculty of Sciences of the University of Cluj. Now Cluj had, with the rest of Transylvania, been incorporated into Romania with the Treaty of Trianon in 1919. The University in Cluj, which had been named the Franz Joseph University since 1881, became a Romanian institution and was officially opened as such by King Ferdinand on 1 February 1920. Angheluță was fully involved in the intense work of organizing mathematical education at the University. Here he joined colleagues Nicolae Abramescu, Petre Sergescu, Gheorghe Bratu and the Director of the Mathematical Seminar, Dimitrie Pompeiu.

Professor Theodor Angheluță was the dean of the Faculty of Sciences of the University of Cluj between 1931 and 1932. In August 1940, after the start of World War II, the north-west part of Romania (including Cluj) was surrendered to Hungary in the Vienna Dictate. This was a decision taken in Vienna under severe pressure from the German Third Reich. The Romanian university in Cluj moved to Alba-Iulia, Turda, Sibiu and Timișoara. In fact the Faculty of Sciences was moved to Timișoara, while the rest of the faculties were moved to Sibiu. All of them began operating in November 1940 and at this time Angheluță taught at Timișoara. He was elected to the Romanian Academy of Sciences on 7 June 1943 and, at his election, his institution is given as Cluj-Timișoara. In 1945, following the end of World War II, the Romanian University returned to Cluj and was named Babeș University (after the Romanian natural scientist Victor Babeș).

Angheluță retired on 1 September 1947, but then, at the end of 1950, he was appointed again as a full professor at the Faculty of Mathematics and Physics at the Victor Babeș University of Cluj. After retiring, he was elected to the Romanian Academy of Sciences in 1948. From 1 October 1955 to September 1962, Professor Theodor Angheluță was a full professor in the Mathematics Department of the Technical Institute of Cluj. He was named 'Scientist emeritus' on 1 January 1963.

Theodor Angheluță made important contributions to Function Theory, to Differential and Integral Equations, and to Functional and Algebraic Equations. A special kind of functional equation is today named after him, namely the 'Angheluță type functional equation'. We now list twenty-one of Angheluță's papers, giving a little more information for some of them:
1. On some integrals (Romanian) (1935) - Corrects results by the mathematician Michel Ghermanescu (1899-1962) published in Gazeta Matematica;
2. Determination of projective transformations which leave invariant a second degree equation (Romanian) (1937) - Angheluță determines the projective transformations which convert a given quadratic equation into a given second order equation;
3. Discussion of the reality of the roots of equations of the third and fourth degree with real coefficients (Romanian) (1938) - Systematic specification of reality conditions and intervals for the roots of equations of the third and fourth degree;
4. About the sum of the roots of a polynomial (Romanian) (1939);
5. On absolute values of the zeros of polynomials (Romanian) (1939);
6. Forming the quotient of two polynomials, and the remainder, if the divisor is factored first degree (Romanian) (1940);
7. Remarques sur des mouvements tautochrones (1941) - Uses methods that were developed by Paul Appell in his book Mécanique Rationelle ;
8. Une identite entre nombres complexes et un théorème de géométrie élémentaire (1941);
9. On orthogonal transformations whose matrices are symmetric (Romanian) (1941) - Angheluță gives a transformation, which depends on $n-1$ real parameters, which is the most general linear transformation satisfying the properties of being orthogonal and having symmetric matrix;
10. Une identité entre nombres complexes et un théorème de géométrie élémentaire (1942) - Angheluță generalises to polygons with $n$ sides, results proved for $n = 3, 4$ by Tiberiu Popoviciu in 1936;
11. Life and mathematical work of Émile Picard (Romanian) (1942) - a nice obituary of Émile Picard who was Angheluță's advisor while he was in France.
12. Circuit transformations characterized by a functional equation (Romanian) (1946);
13. Applications of the divided difference, made as an integral (Romanian) (1952);
14. On a functional equation (Romanian) (1959);
15. On a class of integrals (Romanian) (1959) - The results are obtained via applications of the theory of Bernoulli numbers and the calculus of residues;
16. Remarks concerning Poisson's functional equation (Romanian) (1959);
17. The functional equation of a translation (Romanian) (1959) - proves results by J Aczel in a simpler way.
18. On a functional equation with three unknown functions (Romanian) (1960);
19. A functional equation for the sine and another for a hyperbolic sine (Romanian) (1961) - gives simpler proofs of results already known;
20. The functional equation of the logarithm (Romanian) (1961) - gives simpler proofs of results already known;
21. About a functional equation (Romanian) (1962) - gives simpler proofs of results already known.
We note that this represents only small selection from the papers that Angheluță published. The book [1] contains seventy of Angheluță's papers. He was an excellent teacher and also published a number of books, based on the lecture courses that he gave at the University of Cluj. These, all written in Romanian, include: Course on rational mechanics (1926); Applications of mechanics (1927); Course on higher algebra (1940); Course on the theory of functions of a complex variable (1940); and Analytics (1945).

Theodor Angheluță died at Cluj in May 1964.

### References (show)

1. D Ionescu (ed.), T Angheluță, Mathematical works (Romanian) (Editura Academiei Republicii Socialiste România, Bucharest, 1970).
2. H Wussing and M Köstler (eds.), J C Poggendorff, Biographisch-literarisches Handwörterbuch der exakten Naturwissenschaften. Band VIII Teil 1 Lieferung 2 (Akademie Verlag, Berlin, 1996).
3. N Both, Theodor Angheluță 1882-1964, Teachers of the Cluj School of Mathematics and Computer Science, Babeș-Bolyai University Cluj-Napoca. http://www.cs.ubbcluj.ro/profesor-theodor-angheluta/
4. D I Duca and A Petrusel, Mathematics Education in Romanian at Babeș-Bolyai University Cluj-Napoca, Proceeding 8th Conference on History of Mathematics & Teaching of Mathematics, 21-25 May 2014, Cluj-Napoca, Romania.
5. N Ghircoiașiu and D V Ionescu, The life and works of Theodor Angheluță, in T Angheluță, Mathematical works (Romanian) (Editura Academiei Republicii Socialiste România, Bucharest, 1970).