Gheorghe Călugăreanu (16 June 1902 – 15 November 1976) was a Romanian mathematician, professor at
BabeÈ™-Bolyai University, and full member of the
Romanian Academy.
He was born in
Iași, the son of physician, naturalist, and physiologist
Dimitrie Călugăreanu. From 1913 to 1921 he studied at the
Gheorghe Lazăr High School in
Bucharest
Bucharest ( , ; ) is the capital and largest city of Romania. The metropolis stands on the River Dâmbovița (river), Dâmbovița in south-eastern Romania. Its population is officially estimated at 1.76 million residents within a greater Buc ...
, after which he attended
University of Cluj, graduating in 1924. In 1926 he went to
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
to pursue his studies at the
Sorbonne, supported by a scholarship from the Romanian government.
He obtained his Ph.D. in mathematics in 1929, with thesis ''Sur les fonctions polygènes d'une variable complexe'' written under the direction of
Émile Picard and defended before a jury that also included
Édouard Goursat and
Gaston Julia. After returning to Romania, he was appointed assistant the University of Cluj in 1930; he was promoted to lecturer in 1934 and named professor in 1942. From 1953 to 1957 he served as Dean of the Faculty of Mathematics.
His Ph.D. students include
Petru Mocanu.
He was elected a corresponding member of the Romanian Academy in 1955, and he became a full member in 1963.
Călugăreanu studied the theory of
functions of a complex variable (
meromorphic functions,
univalent functions,
analytic extension invariants), as well as
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 ...
and
algebraic topology, especially in
knot theory. In his best-known work,
he established in 1961 the following foundational result regarding the
writhe of a
knot: take a
ribbon in
three-dimensional space, let
be the
linking number of its border components, and let
be its total
twist; then the difference
depends only on the core curve of the ribbon.
In a paper from 1959,
he showed how to calculate the writhe of a knot by means of a Gaussian
double integral. Călugăreanu's formula has since been pursued by James H. White and F. Brock Fuller, leading to applications in
DNA topology, where writhe is used to describe the amount a piece of
DNA is deformed as a result of
torsional stress (a phenomenon known as
DNA supercoiling). The topological interpretation of
helicity in terms of the Gauss linking number and its limiting form has been called the "Călugăreanu invariant" by
Keith Moffatt and
Renzo L. Ricca.
He died of cancer in
Cluj-Napoca in 1976; following his wishes, he was cremated and the urn was deposited at
Bellu Cemetery in Bucharest.
Publications
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References
External links
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{{DEFAULTSORT:Calugareanu, Gheorghe
1902 births
1976 deaths
Scientists from Iași
Gheorghe Lazăr National College (Bucharest) alumni
BabeÈ™-Bolyai University alumni
Academic staff of BabeÈ™-Bolyai University
20th-century Romanian mathematicians
Complex analysts
Topologists
Titular members of the Romanian Academy
Deaths from cancer in Romania
Burials at Bellu Cemetery