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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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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

  • 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


Roman Numeral Uses

  • Order of Rulers and ships

  • Cornerstones

  • Gravestones

  • Language in Latin roots

  • Number values


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


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


Pi

  • Pi is the ratio of the circumference of a circle to its diameter

  • Always same number

  • Egyptians and Babylonians

  • Above 3 (3.14)


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’


Zero

0

  • Empty space indicator

  • A number itself

  • Concrete to abstract

  • Babylonians and their wedges

  • Punctuation mark


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


Euclid Elements

  • Geometry Applet

  • Beautiful

  • Influential

  • Euclid

  • Logical Development of Geometry


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


Greek Mathematics

  • Impressive civilization

  • Influential

  • Decisive in mathematics

  • Byzantine Greek codices

  • Arabic translations


Schools of Greek Mathematics

  • Ionian School

  • Pythagorean School

  • Eleatic School

  • Sophist School

  • Platonic School

  • School of Eudoxus

  • School of Aristotle


Ionian School

  • Founded by Thales

  • First deductive proofs

  • Anaximander

  • Anaximenes


Pythagorean School

  • Founded by Pythagores

  • Philosophy

  • Proportion

  • Number theory

  • Theory of proof

  • Incommensurables


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


Sophist School

  • Centered in Athens

  • Abstract reasoning

  • Mathematics to understand universe

  • Doubling cube, squaring the circle, trisecting an angle


Platonic School

  • Founded by Plato

  • Conics Menaechmus

  • Asymptotes

  • Intersecting of the parabola and the hyperbola


School of Eudoxus

  • Founded by Eudoxus

  • Proportion

  • Magnitude

  • Proof on quadrature of circle

  • Theorems of plane geometry


School of Aristotle

  • Called Lyceum

  • Founded by Aristotle

  • Philosophy of physics

  • Theoretical

  • Productive

  • Practical


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


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


Presented By: Haley Bacon

  • For more information on the History of Mathematics log onto this website

  • Math is FUN!!!!!


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