Reflective Essay Step 2: Intro/Thesis

 

Much of modern day mathematics is either directly from, or is derived from the theories and advancements from Greek culture. Daily Greek life revolved around mathematics so it was only natural that so many great advancements came from one culture The Greeks developed “equations” for areas, volumes, and angles. The Greeks also, over a long period of time and input from many mathematicians, developed an extremely accurate value for pi. Greek mathematicians also brought in the advancements from of other cultures, such as those from Indian and the Middle East, and applied them to their own developments.

Reflective Essay Part 1- Ellis, CW

Egypt:

  • Number system base 10
  • Used doubling, unit fractions and 2/3
  •  linear & quadratic equations through false position
  • pi=3.160493827

*Pertinent assignments

  • Midterm
  • Chapter 1 HW

Babylonians/Mesopotamia:

  • Sexadecimal system(base 60)
  • diameter=1/3(circumference), area= 1/12(circumference)^2
  • barge area=1/72(circumference)^2, bulls eye area= 1/32 (circumference)^2
  • Pythagorean triples
  • False position
  • Quadratic formula

*Pertinent assignments

  • Library Assignment 2
  • Midterm
  • Cultural Essay 2

Greek:

  • Pythagoras-theorem, etc.
  • Squaring Circle, Doubling Cube, Trisecting general angle
  • Hippocrates
  • Aristotle-symbols
  • Euclid-The Elements, triangle, geometry polygons, pi
  • Method of Exhaustion
  • Theaetetus
  • Archimedes-the method, three propositions for circle(pi), spirals,  induction
  • Apollonius-conics
  • Eratosthesus
  • Hipparchus
  • Ptolemy-Mathematical Collection, cords, etc
  • Diophantus-Arithmetica
  • Pappus
  • Hypatia

*Pertinent assignments

  • Library Assignment 2
  • Midterm
  • Cultural Essay 5
  • Chapter 2 HW
  • Cultural Essay 3
  • Cultural Essay 6
  • Cultural Essay 4
  • Library Assignment 2 (Leonardo de Pisa)
  • Chapter 3 HW

Chinese:

  • Arithmetical Classic…, The Nine Chapters(right triangle, linear eq.,binomial coeff., geometry
  • Liu Hui
  • Gnomons (square roots)
  • Zu Chang Zhi
  • Jia Xian-polynomial division
  • Marco Polo
  • Modular Congruence
  • Remainder Theorem

*Pertinent Assignments

  • Cultural Essay 7
  • Midterm
  • Chapter 5 HW

India:

  • Vedas
  • Alexander the Great
  • Hindu numerals
  • Brahmagupta-Correct Astronomical System of Brahm”
  • The Indian Mathematics
  • Bhaskara
  • Combinatorics
  • Half cord for trig

*Pertinent Assignments

  • Midterm
  • Chapter 6 HW

Islam

  • No decimals, number system ten, fractions
  • Al-Khwazarzini-algebra
  • Omar Al-Khayyan
  • Combinatorics
  • Ahmal ab’du I’n Mun’im
  • Al-Biruni
  • Al-Kashi

 

*Pertinent Assignments

  • Chapter 7 HW