Alexandru Froda Explained

Alexandru Froda (July 16, 1894 – October 7, 1973) was a Romanian mathematician with contributions in the field of mathematical analysis, algebra, number theory and rational mechanics. In his 1929 thesis he provided the namesake proof of an often unnamed theorem now sometimes called Froda's theorem.

Life

Alexandru Froda was born in Bucharest in 1894. In 1927 he graduated from the University of Sciences (now the Faculty of Mathematics of the University of Bucharest). He received his Ph.D. from the University of Paris in 1929 under the direction of Émile Borel.^[1]

Froda was elected president of the Romanian Mathematical Society in 1946. In 1948 he became professor in the Faculty of Mathematics and Physics of the University of Bucharest.

Work

Froda's major contribution was in the field of mathematical analysis. His first important result^[2] was concerned with the set of discontinuities of a real-valued function of a real variable. In this theorem Froda proves that the set of simple discontinuities of a real-valued function of a real variable is at most countable.

In a paper^[3] from 1936 he proved a necessary and sufficient condition for a function to be measurable. In the theory of algebraic equations, Froda proved^[4] a method of solving algebraic equations having complex coefficients.

In 1929 Dimitrie Pompeiu conjectured that any continuous function of two real variables defined on the entire plane is constant if the integral over any circle in the plane is constant. In the same year^[5] Froda proved that, in the case that the conjecture is true, the condition that the function is defined on the whole plane is indispensable. Later it was shown that the conjecture is not true in general.

has at least two solutions passing through every point in the plane.

In the theory of numbers, beside rational triangles^[7] he also proved several conditions^{[8] [9] [10] [11] [12]} for a real number, which is the limit of a rational convergent sequence, to be irrational, extending a previous result of Viggo Brun from 1910.^[13]

In 1937 Froda independently noticed and proved the case

of the Borsuk–Ulam theorem. He died in Bucharest in 1973.

See also

• Froda's theorem

Notes and References

1. Web site: Sur la distribution des propriétés de voisinages des fonctions de variables réelles. Alexandre Froda. Sudoc .
2. Alexandre . Froda . Sur la distribution des propriétés de voisinage des functions de variables réelles . Hermann . Paris . 3 December 1929 . 55.0742.02.
3. Froda . A. . Propriétés caractérisant la mesurabilité des fonctions multiformes et uniformes des variables réelles . . 1936 . 203 . 1313–1315 . 0015.39905.
4. Froda . A. . Résolution générale des équations algébriques . . 1929 . 189 . 523–525.
5. A. Froda, Sur la proprieté de D. Pompeiu, concernant les integrales des fonctions a deux variables réelles, Bulletin de la Société Roumaine des Sciences, Bucharest, 1935, vol. 35, 111-115.
6. A. Froda, Ecuații diferentiale Lavrentiev și funcții Pompeiu, Buletin științific – Academia Republicii Populare Române, nr. 4, 1952, 801-814.
7. A. Froda, Triunghiuri Raționale, Comunicări Academia Republicii Populare Române, nr. 12, 1955
8. A. Froda, Critères paramétriques d'irrationallité, Mathematica Scandinavica, Kovenhava, vol. 13, 1963
9. A. Froda, Sur l'irrationalite des nombres reels, definis comme limite, Revue Roumanie de mathématique pures et appliquées, Bucharest, vol.9, facs.7, 1964
10. A. Froda, Extension effective de la condition d'irrationalité de Vigg Bran, Revue Roumaine de mathématique pures et appliquées, Bucharest, vol. 10, no. 7, 1965, 923-929
11. A. Froda, Sur le familles de critères d'irrationalité, Mathematische Zeitschrift, 1965, 89, 126–136
12. A. Froda, Nouveaux critères parametriques d'irrationalité, Comptes rendus de l'Académie des Sciences de Paris, vol. 261, 338–349
13. Viggo Brun, Ein Satz uber Irrationalitat, Aktiv fur Mathematik, 09 Naturvidensgab, Kristiania, vol. 31, H3, 1910.