Giovanni Vacca
Encyclopedia
Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian
mathematician
, Sinologist and historian of science.
Vacca studied mathematics and graduated from the University of Genoa
in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin
and became an assistant to Giuseppe Peano
. In 1899 he studied, at Hanover
, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin
. He took private lessons of Chinese and continued to study it at the University of Florence
. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number
iteration for pi
:
, 
.
The calculation efficiency of these formulas is significantly worse than of the modern Borwein's algorithm
– they converge by only about half a decimal point with each iteration.
Vacca published his two major contributions to mathematics in 1910 and 1926, on series expansion
(later named Vacca series) of the Euler constant. They are, respectively
Vacca noted in 1910 that:
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, Sinologist and historian of science.
Vacca studied mathematics and graduated from the University of Genoa
University of Genoa
The University of Genoa is one of the largest universities in Italy.Located in Liguria on the Italian Riviera, the university was founded in 1471. It currently has about 40,000 students, 1,800 teaching and research staff and about 1,580 administrative staff.- Campus :The University of Genoa is...
in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
and became an assistant to Giuseppe Peano
Giuseppe Peano
Giuseppe Peano was an Italian mathematician, whose work was of philosophical value. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in...
. In 1899 he studied, at Hanover
Hanover
Hanover or Hannover, on the river Leine, is the capital of the federal state of Lower Saxony , Germany and was once by personal union the family seat of the Hanoverian Kings of Great Britain, under their title as the dukes of Brunswick-Lüneburg...
, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
. He took private lessons of Chinese and continued to study it at the University of Florence
University of Florence
The University of Florence is a higher study institute in Florence, central Italy. One of the largest and oldest universities in the country, it consists of 12 faculties...
. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
iteration for pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
:
, .The calculation efficiency of these formulas is significantly worse than of the modern Borwein's algorithm
Borwein's algorithm
In mathematics, Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/π.-Jonathan Borwein and Peter Borwein's Version :Start out by setting A &= 63365028312971999585426220 \\...
– they converge by only about half a decimal point with each iteration.
Vacca published his two major contributions to mathematics in 1910 and 1926, on series expansion
Series expansion
In mathematics, a series expansion is a method for calculating a function that cannot be expressed by just elementary operators . The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function...
(later named Vacca series) of the Euler constant. They are, respectively
Vacca noted in 1910 that:
- There is some hope that this series can be of some use in the proof of the irrationality of
, a very difficult problem, proposed, but not resolved, in the Correspondence, recently published, between HermiteCharles HermiteCharles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
und StieltjesThomas Joannes StieltjesThomas Joannes Stieltjes was a Dutch mathematician. He was born in Zwolle and died in Toulouse, France. He was a pioneer in the field of moment problems and contributed to the study of continued fractions....
.