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Mathmatics in Ancient Greece

A Curious History of Mathmatics
created by Jongha Hwang September 05, 2016 13:47 pm
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Mathmatics in Ancient Greece

 

Thales

  • the first person to prove the truth of the theorem
  • a theorem(정리, principle) is a statement or hypothesis that can be proved, based on accepted asioms(laws of mathmatics)
  • he determined the height of the Great Pyramid of Giza using its shadow









    his famous theorem
  • the base angles of an isosceles triangle are equal
  • when two straight lines interset, the opposing angles are equal
  • an angle in a semicircle is a right angle

     
  • "geometry" comes from Greek word, geo, which means "earth", and metria meaning "measurement"
  • Thales first created an abstract principle and axioms from examples by deductive reasoning
 

 

 
Pythagoras
  • figurate numbers
  • perfect numbers 1 + 2 + 3 = 6 is a perfect number
  • pythagorean theorem was not actually discovered by Pythagoras. It was known to the Babylonians at least 1,000 years earlier
  • Pythagoras was the first person to prove it.
  • Euclid's Element proposition 47
 
 
The Pythagorean Theorem
 
 
 
 
 
 
 

 

 
Greek Mathmatics
 
Achilles and the Tortoise
  • Zeno if Ekea introduced the notion of infinity with his famouse paradoxes

Plato and his solid

  • he believed that geometry held sacred truths describing the underlying nature of reality
  • when he founded a school called Academy in 387 BCE, the sign above the entrance said:

    Let no one ignorant of geometry enter here


 
 
Eudoxos 
  • one of the most significant mathematicians to attend Plato's Academy
  • he created a type of calculus used to find the area under a curve, developing the method of exhaustion
  • he used his early form of calculus to prove that volume of the pyramid is one-third of prisms
  • also the volume of cone is one-third of cylinder

    The method of exhaustion
    • The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
 
The Three Classical Problems
  1. Squaring the circle means drawing a square with the same are as a given circle - pi came from this try.
  2. Doubling the cube means trying to construct a cube with precisely double the volume of another cube
  3. Trisecting the angle means constructing an angle that is precisely one-third of a given angle
     
  4. all three of the classical problems have no solution
 
 
Euclid and His Elements
 
  • he lived in Alexandria
  • the father of geometry 
  • he compiled all kinds of geometry theorems
  • and wrote a book called, The Elements of Geometry, which became the most translated, published and studied book in the western world, second only to the Bible. the most famous textbook in history.




     
  • Khan Ademy Lecture
     
  • he started with basic assumptions, which are called axioms or postulates.
    from them he proved a proposition, which is called theorem
    no one has done this before
  • if you did not read this book you were not considered as intellect or educated
  • What Euclid did was to really tighten our reasoning to prove something.
  • Arithmatic is just computation. Euclidean geometry is real mathmatics is about.
    making some assumptions and then deducing other things from those assumptions

 

The Hellenistic period 

  • The Hellenistic period covers the period of ancient Greek (Hellenic) history and Mediterranean history
    between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire.
  • At this time, Greek cultural influence and power was at its peak in Europe, Africa and Asia
  • The Hellenistic period saw the rise of New Comedy, Alexandrian poetry, the Septuagint and the philosophies of Stoicism and Epicureanism.
  • Greek Science was advanced by the works of the mathematician Euclid and the polymath Archimedes.

 

Archimedes

  • he came up with the idea, not in a bath tub, but in an attempt to build a huge ship, Syracusia
  • ancient Greek ship sometimes claimed to be the largest transport ship of antiquity.
    She only sailed once, from Syracuse in Sicily to Alexandria in the Ptolemaic Kingdom.




     
  • Law of Buoyancy or Archimedes' Principle
    basically you need as much water as the weight of floating object
  • he also invented Archimedes Screw


     
    a machine historically used for transferring water from a low-lying body of water into irrigation ditches. Water is pumped by turning a screw-shaped surface inside a pipe.



 

 

 

Eratosthenes

  • a contemporary of Archimedes
  • he measured the circumference of the earth


     
  • when he calculate this, he used two propositions from Euclid