17th century of Mathematics

• It is impossible to say with truth that this century or that is the greatest in development of any human interest, but it is entirely within the range of truth to assert that few if any century did so much for mathematicians as that one wich saw :

• Fermat being the modern theory of noumbers;• Descartes and Harriot, invent the analytic geometry;• Cavalieri paved the way for Newton and Leibniz, who, in their

turn established the calculus;• Pascal and Desargues open new fields for pure geometry;• Napier reveal to the world a new method of computation;• And many other brilliant scolars applied the theory developed to

study of curves, to difficult problems, and to study the science of celestial mechanics.

• Printing started to show its power because people in general started to think, and scolars could spread their knowledge not only to people who heard them as before.

• And what is most horrible discoveries of this century were used three houndret years later in the great World War.

Mathematics began to expand into new areas

Blaise Pascal(1623 - 1662)

• was a French mathematician, physicist, and religious philosopher

• he made important contributions to the construction of mechanical calculators

• 1654 he laid down the principles of the theory of probabilities, strongly influencing the development of modern economics and social science

Pascal triangle

Fibonacci SequenceTry this: make a pattern by going up and then along, then add up the squares (as illustrated) ... you will get the Fibonacci Sequence.

(The Fibonacci Sequence is made by adding the two previous numbers, for example 3+5=8, then 5+8=13, etc)

Horizontal SumsWhat do you notice about the horizontal sums?

It doubles each time (powers of 2).

Gamebling

Two players of equal skill want to leave the table

before finishing their game. In what proportion they

should divide the stakes?

• Pascaline

• 1642 Pascal’s calculator

• The Musee des Arts et Metiers in Paris

• Zwinger museum in Dresden

Pierre de Fermat ( 1601 – 1665)

• was a French lawyer and a mathematician who is given credit for early developments that led to modern calculus

• he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus

• theory of numbers• Independently of Descartes, he

discovered the fundamental principles of analytic geometry.

• With Blaise Pascal, he was a founder of the theory of probability.

Fermat’s Last Theorem

the most famous solved problem in the history of mathematics

If an integer n is greater than 2, then the equation

has no solutions in non-zero

integers x, y, and z.

1640, Fermat wrote in the margin in his copy of the Arithmetica

1995, correct proof was finally published by Andrew Wiles

Renѐ Decartes (1596.–1650.)- modern philosophy and modern mathematics- he studied classics, logic and traditional Aristotelian philosophy at the Jesuit college of La Flèche in Anjou. He also learnt mathematics.- in Paris he cultivate the study of geometry- lived and worked all over the world- focused on philosophy- He attempted to justify certain basic beliefs about human beings, the world, and God using a technique of systematic doubt that he invented. - He developed the first modern theory that mind and body are essentially different substances, a distinction that has occupied philosophers

Descartes’s Geometry - a small handbook of only about a hundred pages, that analytic geometry first appeared in print

- the fundamental idea in Descartes’s mind was the elucidating of algebra by means of geometric intuition and concepts

- He began by extending the ancient idea of latitude and longitude 

Bonaventura Cavalieri (1598 .– 1647.)

- Jesuit, professor of mathematics at the University of Bologna

- wrote on conics, trigonometry, optics, astronomy and astrology

-recognized the great value of logarithms

-his greatest contribution was his principle of indivisibles

Cavalieri’s principle

-Bonaventura Cavalieri observed that figures (solids) of equalheight and in which all corresponding cross Sections match in length (area) are of equal area (volume).

For example, take a regular polygon equal in area to an equilateral triangle; erect a pyramid on the triangle and a conelike figure of the same height on the polygon; cross sections of both figures taken at the same height above the bases are equal; therefore, by Cavalieri’s theorem, so are the volumes of the solids.

Guillaume de L’Hospital (1661.-1704.)

- he wrote on geometry, algebra, mechanics

-solved a difficult problem about cycloids posed by Pascal

-published the first book ever on differential carculus

- In this book, l'Hospital included L’ Hospital’s rule 

Isaac Newton• Newton and Leibniz

developed infinitesimal calculus independently, using their own unique notations.

• generalised binomial theorem,

• discovered Newton's identities, Newton's method,

• contributions to the theory of finite differences.

Gottfried Wilhelm, Freiherr von Leibniz

• Leibniz is credited, along with Isaac Newton, with the discovery of infinitesimal calculus.

• He was in a dispute with Newton about

• He had a trial with Newton for infinitesimal calculus He introduced several notations used to this day:

• integral sign ∫ representing an elongated S, from the Latin word summa,

• d used for differentials, from the Latin word differentia.

Newton-Leibnitz’s formula

Connection between mathematics and physics

Daniel Bernoulli• -was s Dutch-Swiss

mathematician and was one of mathematicians in the Bernoulli family

• -he is particulary remembered for his applications of mathematics to mehanics, especially fluid mehanics

• -Bernoulli`s principle is named after Bernoulli published his principle in his book Hydrodinamica

• -Bernoulli`s principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli`s equation

Johannes Kepler

• was a German mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution

• Kepler`s laws of planetary motion are three mathematicial laws that describe the motion of planets in the Solar System

• his book “A New Astronomy” including the first two laws of planetary motion

Galileo Galilej

• Was a mathematician, astronomer, physicist and philosopher who played a major role in the Scientific Revolution

• - Galileo produced one piece of original and even prophetic work in mathematics: Galileo`s paradox which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares

Made by:

Ana Cenkovčan

Anita JukićŽeljka KraljićAntun

MikolaševićDino Dušanić

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