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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.

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History Of Mathematics

  1. 1. History of Mathematics<br />Prentice Hall Geometry<br />Geometry<br />August 2009<br />
  2. 2. Mayans <br />MEXICO<br />Mayans are from ____________.<br />Base 20 system<br />One of the 1st cultures to invent _________.<br />Their calendar had 18 months a year; 20 days a month<br />ZERO<br />
  3. 3. According to the Mayans:<br />The WORLD will END on… <br />The WORLD will END on… <br />21 DECEMBER 2012<br />
  4. 4. Romans<br />Roman Numeral System<br />I, II, III, IV, V,…,X, L, C, D, M,…<br />The system is based on Subtractive Pairs<br />The Line above Roman Numerals means multiply by a thousand<br />
  5. 5. Egyptians<br />1st to have fractions! <br />Geometry invented by Egyptians<br />Geo means earth; meter comes from measures<br />Used geometry to measure land to assess taxes<br />
  6. 6. Egyptians<br />Came closest to developing pi <br />pi is the ratio of diameter of a circle to the circumference of the circle<br />
  7. 7. Famous Mathematicians<br />Rene Descartes<br />Pierre de Fermat<br />Blaise Pascal<br />Robert Hooke<br />Isaac Newton<br />James Bernoulli<br />GirolamoSaccheri<br />John Bernoulli<br />Christian Goldbach<br />Leonhard Euler<br />Joseph Louise Lagrange<br />Carl Freidrich Gauss<br />Bernhard Riemann<br />David Hilbert<br />John von Neumann<br />Thales of Miletus<br />Pythagoras of Samos<br />Hippocrates of Chios<br />Euclid<br />Archimedes<br />Galileo Galilei<br />
  8. 8. QUIZ<br />Quiz<br />When is the world going to end according to the Mayans?<br />Where are the Mayans from?<br />What is the system of Roman Numerals based on?<br />Egyptians invented _______ for what two reasons?<br />What base system do we use today?<br />
  9. 9. Geometry <br />Three Types of Geometry:<br />Euclidean (what we will study)<br />Non- Euclidean <br />Elliptic Geometry (Spherical Geometry)<br />Hyperbolic Geometry<br />
  10. 10. EuclideanGeometry<br />
  11. 11. Undefined Terms can be <br /> described but cannot be <br /> given precise definitions using <br /> simpler known terms.<br />3 Main Undefined Terms:<br />Undefined Terms<br />Point is thought to be a circular<br /> dot that is shrunk until it has no size. <br />Line is thought to be a wire stretched<br /> as tightly as possible of infinite length <br />having no thickness.<br />Plane is thought to be a sheet of paper that <br />has no thickness, stretched tightly , and <br />extending infinitely in all directions.<br />
  12. 12. Using the undefined terms (point, line, plane)<br />allows us to define other terms in geometry, <br />e.g. space: a set of all points<br />Definitions<br />
  13. 13. Postulates and axioms are one in the same.<br />They are accepted as statements of fact.<br />Postulates and Axioms<br />
  14. 14. Theorems<br />Theorems are results that are deduced from undefined terms, definitions, postulates, <br />and/ or <br />results that follow from them.<br />
  15. 15. EuclideanGeometry<br />
  16. 16. how to solve geometry?<br />Scientific Method?<br />Ask a Question<br />Do Background Research<br />Construct a Hypothesis<br />Test Your Hypothesis by Doing an Experiment<br />Analyze Your Data and Draw a Conclusion<br />Communicate Your Results<br />
  17. 17. how to solve geometry?<br />Four Steps:<br />Understand the Problem<br />Devise a Plan<br />Carry Out the Plan<br />Look Back<br />
  18. 18. 1. Understand the Problem<br />Is it clear to you what is to be found?<br />Do you understand the terminology?<br />Is there enough information?<br />Is there irrelevant information?<br />Are there any restrictions or special conditions to be considered?<br />
  19. 19. 2. Devise a Plan.<br />How should the problem be approached?<br />Does the problem appear similar to any others you have solved?<br />What strategy might you use to solve the problem?<br />
  20. 20. 3. Carry Out the Plan<br />Apply the strategy or course of action chosen in Step 2 until a solution is found or you decide to try another strategy<br />
  21. 21. 4. Look Back<br />Is your solution correct?<br />Do you see another way to solve the problem?<br />Can your results be extended to a more general case?<br />
  22. 22. Some Strategies…<br />Draw a picture!<br />Guess and check.<br />Use a variable.<br />Look for a pattern.<br />Make a table.<br />Solve a simpler problem.<br />
  23. 23. What to do when you start working a geometry problem?<br />Understand the problem.<br />Devise a plan.<br />Carry out the plan.<br />Look Back.<br />
  24. 24. POINT<br />LINE<br />B<br />A<br />A<br />l<br />AB<br />Line l<br />
  25. 25. plane<br />B<br />A<br />C<br />Plane ABC or Plane P<br />P<br />

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