In 1934, Barbilian published his article describing metrization of a region K, the interior of a simple closed curveJ. Let xy denote the Euclidean distance from x to y. Barbilian's function for the distance from a to b in K is At the University of Missouri in 1938 Leonard Blumenthal wrote Distance Geometry. A Study of the Development of Abstract Metrics, where he used the term "Barbilian spaces" for metric spaces based on Barbilian's function to obtain their metric. And in 1954 American Mathematical Monthly published an article by Paul J. Kelly on Barbilian's method of metrizing a region bounded by a curve. Barbilian did not have access to these publications, but he did read Blumenthal in Mathematical Reviews. He answered in 1959 with an article which described "a very general procedure of metrization through which the positive functions of two points, on certain sets, can be refined to a distance." Besides Blumenthal and Kelly, articles on "Barbilian spaces" have appeared in the 1990s from Patricia Souza, while Wladimir G. Boskoff, Marian G. Ciucă and Bogdan Suceavăwrite inthe 2000s about "Barbilian's metrization procedure". Barbilian indicated in his paper Asupra unui principiu de metrizare that he prefers the term "Apollonian metric space", and articles from Alan F. Beardon, Frederick Gehring and Kari Hag, Peter A. Häströ, Zair Ibragimov and others use that term.
Ring geometry
Barbilian made a contribution to the foundations of geometry with his articles in 1940 and 1941 in Jahresbericht der Deutschen Mathematiker-Vereinigung on projective planes with coordinates from a ring. According to Boskoff and Suceavă, this work "inspired research in ring geometries, nowadays associated with his, Hjelmslev’s and Klingenberg’s names." A more critical stance was taken in 1995 by Ferdinand D. Velkamp: Nevertheless, in 1989 John R. Faulkner wrote an article "Barbilian Planes" that clarified terminology and advanced the study. In his introduction he wrote:
1960: Grupuri cu operatori: Teoremele de descompunere ale algebrei, Editura Academiei, Bucharest, Romania
Academic career
In 1942, Barbilian was named professor at the University of Bucharest, with some help from fellow mathematician Grigore Moisil. As a mathematician, Barbilian authored 80 research papers and studies. His last two papers, written in collaboration with Nicolae Radu, appeared posthumously, in 1962.
Political creed
Barbu was mostly apolitical, with one exception: around 1940 he became a sympathizer of the fascist movementThe Iron Guard, dedicating some poems to one of its leaders, Corneliu Zelea Codreanu. In 1940, he also wrote a poem praising Hitler.
Death
Ion Barbu died in Bucharest in 1961, and is buried at Bellu Cemetery.
Born in Utopia - An anthology of Modern and Contemporary Romanian Poetry - Carmen Firan and Paul Doru Mugur with Edward Foster - Talisman House Publishers - 2006 -
Testament – Anthology of Modern Romanian Verse / Testament - Antologie de Poezie Română Modernă – Bilingual Edition English & Romanian – Daniel Ioniță with Eva Foster and Daniel Reynaud – Minerva Publishing 2012 and 2015 -
Testament - Anthology of Romanian Verse - American Edition - monolingual English language edition - Daniel Ioniță with Eva Foster, Daniel Reynaud and Rochelle Bews - Australian-Romanian Academy for Culture - 2017 -