17th century of Mathematics

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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.

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Mathematics began to expand into new areas
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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

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Pascal triangle
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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
358, then 5813, etc)
Horizontal Sums What do you notice about the
horizontal sums? It doubles each time (powers
of 2).
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GameblingTwo players of equal skill want to
leave the table before finishing their game. In
what proportion they should divide the stakes?

• Pascaline
• 1642 Pascals calculator
• The Musee des Arts et Metiers in Paris
• Zwinger museum in Dresden

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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.

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Fermats Last Theoremthe 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

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Ren? 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

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• Descartess Geometry
• a small handbook of only about a hundred
  pages, that analytic geometry first appeared
  in print
• the fundamental idea in Descartess mind was the
  elucidating of algebra by means of geometric
  intuition and concepts
• He began by extending the ancient idea of
  latitude and longitude 

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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

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• Cavalieris 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 Cavalieris theorem, so
  are the volumes of the solids.

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Guillaume de LHospital (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 Hospitals
  rule
•  

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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.

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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.

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Newton-Leibnitzs formula
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Connection between mathematics and physics
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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
• -Bernoullis principle is named after Bernoulli
  published his principle in his book Hydrodinamica
• -Bernoullis principle can be applied to various
  types of fluid flow, resulting in what is loosely
  denoted as Bernoullis equation

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

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Galileo Galilej
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• 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 Galileos paradox
  which shows that there are as many perfect
  squares as there are whole numbers, even though
  most numbers are not perfect squares

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• Made by
• Ana Cenkovcan
• Anita Jukic
• Željka Kraljic
• Antun Mikolaševic
• Dino Dušanic

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Have a nice dream