PierreSimon Laplace

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Pierre-SimonLaplace

• By
• Lisa Grilliot
• Mary Balmes

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Outline

• Background
• Works
• Bayes Theorem
• Buffon-Laplace Needle Problem

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Background
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• Born March 23, 1749 in Beaumont-en-Auge,
  Normandy, France
• Went to school from age 7-16
• Father wanted him to get involved in the Church
• Age of 16 began study at Caen University where
  two professors discovered his mathematical talent
  

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Background

• Left Caen and went to Paris to pursue his love of
  math
• Introduced to Jean d'Alembert
• Became a professor of mathematics at the École
  Militaire to make money
• Third times a charm for Académie des Sciences
• Arrogant

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Background

• 1784 appointed as examiner at the Royal
  Artillery Corps
• Because of this job, he became well-known to the
  ministers of the government and others who held
  positions of power in France.
• During his time as the examiner, he examined and
  passed the 16 year old Napoleon Bonaparte (in
  1785).

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Napoleon Laplace

• Napoleon You have written this huge book on the
  system of the world without once mentioning the
  author of the universe.
• Laplace Sire, I had no need of that hypothesis.
  (example of his arrogance)
• Later when Napoleon told Lagrange about the
  incident, Lagrange commented Ah, but that is a
  fine hypothesis. It explains so many things.

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Background

• Laplace served on a committee set up to
  investigate the largest hospital in Paris
• Compared mortality rates at the hospital with
  those of other hospitals in France and elsewhere

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Background

• Laplace married on May 15, 1788 at the age of 39
• His wife, Marie-Charlotte de Courty de Romanges,
  was 19.
• They had two children.
• Left Paris in 1793 and returned July 1794

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Background

• 1795 the École Normale was founded with the aim
  of training school teachers
• The École Normale survived for only four months

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Background

• member, then chancellor, of the Senate,
• received the Legion of Honour in 1805.
• However Napoleon removed Laplace from the office
  of Minister of the Interior after only six
  weeks-
• ... because he brought the spirit of the
  infinitely small into the government.

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Background

• Laplace's desire to take a leading role in
  physics led him to become a founder member of the
  Société d'Arcueil in around 1805
• The group strongly advocated a mathematical
  approach to science
• Became Count of the Empire in 1806
• Named a marquis in 1817

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Laplaces Death

• Laplace died on March 5, 1827 in Paris
• Due to his death, the Academy cancelled a meeting
  as a sign of respect.
• What we know is not much. What we do not know is
  immense.

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Traité du Mécanique Céleste

• Laplace's most important work
• Published in 5 volumes, the first two in 1799
• The first volume is divided into two books
• general laws of equilibrium and motion of
  solids and also fluids.
• the law of universal gravitation and the
  motions of the centres of gravity of the bodies
  in the solar system.
• The second volume mechanics applied to a study
  of the planets
• He does not attribute many of the ideas to the
  work of others (Arrogance again?)

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What Laplace is know for.

• Differential equations Laplace Transforms
• Solar systems
• Physics theory of heat
• Probability
• Bayes Theorem
• Central limit theorem

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Introduction to Probability

• Definition of Probability
• Where S is the sample space, or the set of all
  possible outcomes, of the experiment, and A is a
  subset of S.
• Conditional Probability
• (Venn Diagram)
• http//www.funtrivia.com/playquiz.cfm?qid139777o
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Bayes Theorem
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Laplaces Bayes Theorem

• In a bolt factory, 30, 50, 20 of production is
  manufactured by machines I, II, and III
  respectively. If 4, 5, and 3 of the output of
  these machines is defective, what is the
  probability that a randomly selected bolt that is
  found to be defective is manufactured by machine
  III? To solve this problem, let A be the event
  that a random bolt is defective and b3 be the
  event that it is manufactured by machine III.
• Hands on demonstration

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Buffon-Laplace Needle Problem

• Given a floor with a grid of parallel lines
  spaced evenly apart (a being the distance between
  the vertical lines and b being the distance
  between the horizontal lines), what is the
  probability that needle of length
  will intersect one of the grid lines after having
  been dropped on the floor?
• Extension of Buffons Needle Problem

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Graphical Illustrations
Intersection of 2 Partial Cylinders
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Homework Exercises

• 1)Supplies Needed
• Floor covered with 1ft. square tiles
• Ruler
• A pen of approximately normal length
• a) If you would drop this pen onto the tiled
  floor, what is the probability that it would rest
  over a seam in the tile?
• b) Drop the pen on the tiled floor. Did it rest
  over a seam?

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Homework Exercises

• 2)Suppose that 5 of the men and 2 of the women
  working for a corporation make over 120,000 a
  year. If 30 of the employees of the corporation
  are women, what percent of those who make over
  120,000 a year are women?