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History Of Mathematics
 

History Of Mathematics

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This is a brief, I mean brief, introduction to mathematics that I used this year. I also introduced the different types of Geometry, and steps to solving a geometry problem.

This is a brief, I mean brief, introduction to mathematics that I used this year. I also introduced the different types of Geometry, and steps to solving a geometry problem.

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    History Of Mathematics History Of Mathematics Presentation Transcript

    • History of Mathematics
      Prentice Hall Geometry
      Geometry
      August 2009
    • Mayans
      MEXICO
      Mayans are from ____________.
      Base 20 system
      One of the 1st cultures to invent _________.
      Their calendar had 18 months a year; 20 days a month
      ZERO
    • According to the Mayans:
      The WORLD will END on…
      The WORLD will END on…
      21 DECEMBER 2012
    • Romans
      Roman Numeral System
      I, II, III, IV, V,…,X, L, C, D, M,…
      The system is based on Subtractive Pairs
      The Line above Roman Numerals means multiply by a thousand
    • Egyptians
      1st to have fractions!
      Geometry invented by Egyptians
      Geo means earth; meter comes from measures
      Used geometry to measure land to assess taxes
    • Egyptians
      Came closest to developing pi
      pi is the ratio of diameter of a circle to the circumference of the circle
    • Famous Mathematicians
      Rene Descartes
      Pierre de Fermat
      Blaise Pascal
      Robert Hooke
      Isaac Newton
      James Bernoulli
      GirolamoSaccheri
      John Bernoulli
      Christian Goldbach
      Leonhard Euler
      Joseph Louise Lagrange
      Carl Freidrich Gauss
      Bernhard Riemann
      David Hilbert
      John von Neumann
      Thales of Miletus
      Pythagoras of Samos
      Hippocrates of Chios
      Euclid
      Archimedes
      Galileo Galilei
    • QUIZ
      Quiz
      When is the world going to end according to the Mayans?
      Where are the Mayans from?
      What is the system of Roman Numerals based on?
      Egyptians invented _______ for what two reasons?
      What base system do we use today?
    • Geometry
      Three Types of Geometry:
      Euclidean (what we will study)
      Non- Euclidean
      Elliptic Geometry (Spherical Geometry)
      Hyperbolic Geometry
    • EuclideanGeometry
    • Undefined Terms can be
      described but cannot be
      given precise definitions using
      simpler known terms.
      3 Main Undefined Terms:
      Undefined Terms
      Point is thought to be a circular
      dot that is shrunk until it has no size.
      Line is thought to be a wire stretched
      as tightly as possible of infinite length
      having no thickness.
      Plane is thought to be a sheet of paper that
      has no thickness, stretched tightly , and
      extending infinitely in all directions.
    • Using the undefined terms (point, line, plane)
      allows us to define other terms in geometry,
      e.g. space: a set of all points
      Definitions
    • Postulates and axioms are one in the same.
      They are accepted as statements of fact.
      Postulates and Axioms
    • Theorems
      Theorems are results that are deduced from undefined terms, definitions, postulates,
      and/ or
      results that follow from them.
    • EuclideanGeometry
    • how to solve geometry?
      Scientific Method?
      Ask a Question
      Do Background Research
      Construct a Hypothesis
      Test Your Hypothesis by Doing an Experiment
      Analyze Your Data and Draw a Conclusion
      Communicate Your Results
    • how to solve geometry?
      Four Steps:
      Understand the Problem
      Devise a Plan
      Carry Out the Plan
      Look Back
    • 1. Understand the Problem
      Is it clear to you what is to be found?
      Do you understand the terminology?
      Is there enough information?
      Is there irrelevant information?
      Are there any restrictions or special conditions to be considered?
    • 2. Devise a Plan.
      How should the problem be approached?
      Does the problem appear similar to any others you have solved?
      What strategy might you use to solve the problem?
    • 3. Carry Out the Plan
      Apply the strategy or course of action chosen in Step 2 until a solution is found or you decide to try another strategy
    • 4. Look Back
      Is your solution correct?
      Do you see another way to solve the problem?
      Can your results be extended to a more general case?
    • Some Strategies…
      Draw a picture!
      Guess and check.
      Use a variable.
      Look for a pattern.
      Make a table.
      Solve a simpler problem.
    • What to do when you start working a geometry problem?
      Understand the problem.
      Devise a plan.
      Carry out the plan.
      Look Back.
    • POINT
      LINE
      B
      A
      A
      l
      AB
      Line l
    • plane
      B
      A
      C
      Plane ABC or Plane P
      P