Pietro Mengoli
Encyclopedia
Pietro Mengoli was an Italian
mathematician
and clergyman from Bologna, where he studied with Bonaventura Cavalieri
at the University of Bologna
, and succeeded him in 1647. He remained as professor there for the next 39 years of his life.
In 1644 it was Mengoli who first posed the famous Basel problem
, solved in 1735 by Leonhard Euler
.
He wrote a paper in 1650 in which he proved that the sum of the alternating harmonic series is equal to the natural logarithm
of 2.
He also proved that the harmonic series does not converge, and provided a proof that Wallis' product for
is correct.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
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....
and clergyman from Bologna, where he studied with Bonaventura Cavalieri
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri was an Italian mathematician. He is known for his work on the problems of optics and motion, work on the precursors of infinitesimal calculus, and the introduction of logarithms to Italy...
at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
, and succeeded him in 1647. He remained as professor there for the next 39 years of his life.
In 1644 it was Mengoli who first posed the famous Basel problem
Basel problem
The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate...
, solved in 1735 by Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
.
He wrote a paper in 1650 in which he proved that the sum of the alternating harmonic series is equal to the natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
of 2.
He also proved that the harmonic series does not converge, and provided a proof that Wallis' product for
is correct.