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History of Mathematics

History of Mathematics. By: Haley Bacon. Mathematics. Arabic Numerals Roman Numerals Pi Zero Euclid Elements Greek mathematics and schools. Arabic Numerals. Arabs translated Origin is Indian Evolved from letters of the Arabic alphabet Simplified arithmetic. Three types of Arithmetic.

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History of Mathematics

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  1. History of Mathematics By: Haley Bacon

  2. Mathematics • Arabic Numerals • Roman Numerals • Pi • Zero • Euclid Elements • Greek mathematics and schools

  3. Arabic Numerals • Arabs translated • Origin is Indian • Evolved from letters of the Arabic alphabet • Simplified arithmetic

  4. Three types of Arithmetic • Counting on fingers-numerals were written in words. • Sexagesimal System-letters were formed from the alphabet • Arithmetic Indian Numerals and Fractions-the decimal place and value system were formed

  5. Roman Numeral Uses • Order of Rulers and ships • Cornerstones • Gravestones • Language in Latin roots • Number values

  6. Reading Numerals • A letter repeated repeats its value that many times • Letters placed after greater number increases greater number by the smaller • If placed in front it decreases greater value • Bar placed on top increases value by 1000

  7. Arabic and Roman Numerals • The difference between the Roman and Arabic Numerals is that the Romans didn’t have a symbol for zero and the numeral placement within a number can sometimes indicate subtraction rather than addition

  8. Pi • Pi is the ratio of the circumference of a circle to its diameter • Always same number • Egyptians and Babylonians • Above 3 (3.14)

  9. Pi • Pi is an infinite decimal • The ‘p’ stands for perimeter • Numbers to the right of 0 never repeat • No repeating pattern for pi has been discovered • Can be used in probability and ‘famous five’

  10. Zero 0 • Empty space indicator • A number itself • Concrete to abstract • Babylonians and their wedges • Punctuation mark

  11. Zero • Sums of positive and negative numbers with zero • Subtraction of positive and negative numbers with zero • Multiplication and division with positive and negative numbers

  12. Euclid Elements • Geometry Applet • Beautiful • Influential • Euclid • Logical Development of Geometry

  13. Element Propositions • Definition of parallel lines • Axioms for magnitudes • Bisect angles and line segments • Two sides of a triangle will always be greater than one side

  14. Greek Mathematics • Impressive civilization • Influential • Decisive in mathematics • Byzantine Greek codices • Arabic translations

  15. Schools of Greek Mathematics • Ionian School • Pythagorean School • Eleatic School • Sophist School • Platonic School • School of Eudoxus • School of Aristotle

  16. Ionian School • Founded by Thales • First deductive proofs • Anaximander • Anaximenes

  17. Pythagorean School • Founded by Pythagores • Philosophy • Proportion • Number theory • Theory of proof • Incommensurables

  18. Eleatic School • Led by Zeno • Discrete and the continuous • Decomposable and the indecomposable • Motion is continuous and smooth • Zeno’s Paradoxes, Dichotomy,Achilles, Arrow and Spade

  19. Sophist School • Centered in Athens • Abstract reasoning • Mathematics to understand universe • Doubling cube, squaring the circle, trisecting an angle

  20. Platonic School • Founded by Plato • Conics Menaechmus • Asymptotes • Intersecting of the parabola and the hyperbola

  21. School of Eudoxus • Founded by Eudoxus • Proportion • Magnitude • Proof on quadrature of circle • Theorems of plane geometry

  22. School of Aristotle • Called Lyceum • Founded by Aristotle • Philosophy of physics • Theoretical • Productive • Practical

  23. Bibliography Slide 1: Picture-Clip Art Slide 2: None Slide 3: picture and info- http://www.islamicity.org/mosque/ihame/Ref6.htm Slide 4: information-http://www-gap.dcs.st- and.ac.uk/~history/HistTopics/Arabic_numerals.html Slide 5: Information- http://www.novaroma.org/via_romana/numbers/html Picture: http://www.wilkiecollins.demon.co.uk/roman/intro.htm Slide 6: Information- http://www.infoplease.com/ipa/A0001734.html Slide 7: Information- http://www.infoplease.com/ipa/A0001734.html Picture- http://www.wilkiecollins.demon.co.uk/roman/intro.htm Slide 8: Information- http://mathforum.org/dr.math/faq/faq.pi.html Picture-clipart Slide 9: Information- http://mathforum.org/dr.math/faq/faq.pi.html

  24. Cont… Slide 10: Information- http://www-groups.dsc.st-and.ac.uk/history/HistTopics/Zero.html Picture- Word Art Slide 11: Information- http://www-groups.dsc.st-and.ac.uk/history/HistTopics/Zero.html Slide 12: Information- http://aleph0.clarku.edu/~djoyce/java/elements/elements.html Picture-http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html Slide 13: Information and Picture- http://aleph0.clarku.edu/~djoyce/java/elements/trip.html Slide 14-22: All Information and Pictures-http://www.math.tamu.edu/~don.allen/history/greekorg/greekorg.html Slide 15: Animation-http://www.animationfactory.com/free/school/school_page_aa.html Sound- Sound Gallery in Microsoft Slide 25: Picture- Digital Camera Sound- sound gallery from Microsoft

  25. Presented By: Haley Bacon • For more information on the History of Mathematics log onto this website • Math is FUN!!!!!

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