3. LEONARDO
FIBONACCI
Leonardo Fibonacci, son of Guglielmo Bonacci,
was born in Pisa around 1170.
His father was responsible for trade in Pisa
at the colony of Bugia, in Algeria. A few
years after 1192, Leonardo went with his
father to Bugia where he learned
mathematics.
His father wanted Leonardo to become a merchant, so he sent
him on a tour to Egypt, Syria, Greece, Sicily and Provence.
Fibonacci took the opportunity offered by his travels abroad
to study and learn the mathematical techniques used in these
regions and collected them in his book "Liber abbaci",
published in 1228.
He died in Pisa around 1235.
4. THE FIBONACCI
SEQUENCE
The Fibonacci sequence, indicated Fₙ, shows a succession of positive
integers in which each number, starting from the third, is the sum of the
two previous ones, where the first two are:
The elements Fₙ are also called Fibonacci numbers.
7. NICCOLO’
TARTAGLIA
Niccolò Fontana, also known as Niccolò Tartaglia
because of his stuttering, was born in Brescia in 1499.
Tartaglia tells that at 13 years old, during the sack of
Brescia by the French on 19 February 1512, he took
refuge with his family in the old cathedral of Brescia,
but they were followed up there and then attacked:
Niccolò suffered a fracture of the skull and injuries to
the jaw and palate.
It is mainly known for the discovery of
the numerical triangle called "triangle
of Tartaglia", which appears in the
book "General treatise on numbers
and measures" written in 1556; in 1521
it solved the cubic equation.
He died in Venice on 13 December
1557.
8. TARTAGLIA’S
TRIANGLE
The Tartaglia’s triangle is a triangle-shaped table
composed of natural numbers, where each number is a
particular binomial coefficient.
This table has infinite elements and each row
is obtained from the previous. Its main
application lies in the development of any
binomial power:
9. CONSTRUCTION OF THE
TARTAGLIA’S TRIANGLE:
To write the elements that make up the triangle of Tartaglia all the numbers 1 are
shown on the top vertex and along the two sides of the triangle;
Each element is obtained from the sum of the two numbers of the line above it.
11. GALILEO GALILEI
Galileo Galilei was born in Pisa on 15
February 1564. He was an Italian
physicist, astronomer, philosopher,
mathematician and academic,
considered the father of modern
science.
In 1580 he began to study medicine but, a few
years later, he decided to specialize in mathematics
and to undertake the study of physics.
12. Galileo Galilei introduced the
experimental scientific method and
supported the Copernican theory, for
which he was accused of contradicting
the Holy Scriptures and was
condemned by the Court of the Holy
Office.
Galileo Galilei is considered an
important figure in the Scientific
Revolution.
He died on 8 January 1642 in
Arcetri.
THE EXPERIMENTAL
SCIENTIFIC METHOD
13. GALILEO’S INVENTIONS
During his stay in Pisa
came to his first discovery,
the isochronism of the
oscillations of the
pendulum. Going on with his studies,
he formulates some
theorems of mechanics
and geometry until he
discovers the
hydrostatic balance to
calculate the specific
weight of bodies.12
In 1604 a new star
appeared, the Super
Nova. This event led him
to perfect the
telescope, which was
used to observe the
stars.
15. EVANGELISTA
TORRICELLIEvangelista Torricelli was born in Rome
on 15 October 1608.
In Faenza, he went on to study mathematics.
In Rome, for many years Torricelli worked and
studied with Father Castelli who presented to
Galileo his manuscript ‘’De motu gravium’’.
On 10 October 1641 Torricelli became Galileo’s
assistant.
When Galileo died Torricelli became his
successor as mathematician of the Grand
Duchy of Tuscany.
He elaborated several important theorems and anticipated the
infinitesimal calculus, he devoted himself to physics studying
the motion of gravities and fluids and deepening the optics.
He died on 25 October 1647 in Florence
16. TORRICELLI’S TUBE
Torricelli also dedicated himself to the study of fluids, inventing the mercury
barometer called "Torricelli's tube".
This invention is based on the measurement of atmospheric pressure
by a tube that is filled with mercury up to a constant height of 760mm.
mercur
y
mercur
y
vacuum
760mm
__________
17. TORRICELLI’S
TRUMPET
This instrument has the particularity of having
finished volume, but infinite area.
infinitely
Thanks to the integration formulas we can find:
• Volume of solid
• Area of solid
19. PAOLO RUFFINI
Paolo Ruffini was born in Valentano on 22
September 1765.
He is famous for his contributions to Algebra and
in particular for his polynomial division algorithm.
He was an Italian mathematician and physician,
obtaining a degree in Philosophy, Medicine, Surgery
and Mathematics from the University of Modena
in 1788. So from 1797 he was a professor of
Mathematics at the same University.
When the typhus epidemic of 1817 broke out, he
became ill, treating his patients and despite the
recovery he had to leave the chair in 1819.
He died in Modena on 10 May 1822.
20. RUFFINI’S
ROULERuffini was responsible for the so called
Theorem of Abel-Ruffini (demonstration of
the algebraic non solubility of the equations
after the fourth degree) and in 1809, the
publication of Ruffini's rule.
This is a method of dividing polynomials in
which the coefficients of polynomials are
divided, removing the variables and the
exponents, to verify if it is exactly divisible by
a binomial.
22. VITO VOLTERRA
Vito Volterra was born in Ancona on 3 May 1860.
He was an Italian mathematician, physicist,
politician and anti-fascist.
At the age of 13, he calculated the trajectory of
a bullet under the effects of the gravitational
field of the Earth and the Moon.
For two years he devoted himself to partial derivative
equations and particularly to cylindrical wave equations.
He died in Rome on 11 October 1940.
In the University of Pisa, he began the development of the theory of the functional,
dealt with the integral equations and the equations integro-differential.
23. VOLTERRA’S INVENTIONS
• .Functional analysis, is the
field of mathematical analysis
that deals with the study of
spaces of functions;
• .Integral equations, every
equation that has the unknown
under the sign of integral.
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