Transcript Slide 1
17th century of Mathematics
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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
Horizontal Sums
What do you notice about the horizontal sums? It doubles each time (powers of 2).
Fibonacci Sequence
Try 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)
• Pascaline • 1642 Pascal’s calculator • The Musee des Arts et Metiers in Paris • Zwinger museum in Dresden Gamebling Two players of equal skill want to leave the table before finishing their game. In what proportion they should divide the stakes?
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
Ren ѐ Decartes (
1596.–1650.
)
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modern philosophy and modern
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mathematics he studied classics, logic and traditional Aristotelian philosophy at the Jesuit college of La Flèche in Anjou. He also learnt mathematics.
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in Paris he cultivate the study of geometry
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lived and worked all over the world focused on philosophy
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He attempted to justify certain basic beliefs about human beings, the world, and God using a technique of systematic doubt that he invented.
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He developed the first modern theory that mind and body are essentially different substances, a distinction that has occupied philosophers
Descartes’s Geometry
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a small handbook of only about a hundred pages, that analytic geometry first appeared in print
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t he fundamental idea in Descartes’s mind was the elucidating of algebra by means of geometric intuition and concepts
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He began by extending the ancient idea of latitude and longitude
Bonaventura Cavalieri (
1598 .
– 1647.)
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Jesuit, professor of mathematics at the University of Bologna
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wrote on conics, trigonometry, optics, astronomy and astrology
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recognized the great value of logarithms
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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.)
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he wrote on geometry, algebra, mechanics
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solved a difficult problem about cycloids posed by Pascal
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published the first book ever on differential carculus
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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
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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 Jukić Željka Kraljić Antun Mikolašević Dino Dušanić