Lecture 5: Alex the Great, Euclid, Archimedes Flashcards
Alexander the Great’s background?
Actually Macedonian
->father, Philip I of Macedon, was King
->tutored by Aristotle until 16, when he became general
->very big deal, because Aristotle “knows everything”
Ascends after guards assassinate father (King Philip)
->People thought they could break away
Alex invades Greece proper
->Peloponnesian peninsula submits
->Conquers from Greece & Balkans to India’s border
End result is Greek culture is in and draws from a vast swathe of land.
Effects of Alex’s Imperialistic Invasion?
1) Destabilises Athens as centre of power
- >Just another city state
- >no longer where all phils talked
- >pulls on all regions theories
2) Brings Greek philosophy to many people
- >e.g. Egypt became like Greece
- >starts physical modelling
3) Shows Empire building is possible
- >Will influence the Romans
Alexandria?
One of many Alex moulded to his image
->most renamed later on
The one we care about is in Egypt
- > was a “University town”, there for learning
- > many temples and schools to the muses
- > “museum”
- > supported by patronage (donations)
- > freedom to study
Euclid, background and contributions?
From Alexandria (~4th BC - 3rd BC), lots of geometry.
THE FATHER OF MATH
- > gives the rigorous mathematical proof
- > based on AXIOMS
Axioms: Statements that are true without proof
- > self evident
- > everyone understands and assumes true
Gave 5 Axioms:
- > Straight line seg can join any 2 pts
- > straight line can be extended infinitely
- > straight line -> circle with length = radius
- > right angle congruence
- > parallel postulate
Archimedes, background and contributions?
From Syracuse, Italy (~3rd C), but likely in Alexandria
->used similar methods to Euclid
Master mathematician (geometry) also practical uses!
- > developed mathematical devices (e.g. Arch. screw)
- > to understand the natural world
- > inventions wouldn’t have been possible w/o math
- > screw had specific angles
- > mirrors to burn Roman ships
- > might be involved in the space analog model?
POLYMATH ENGINEER, FATHER OF ENGINEERING
- > very practical (creates Law of the Lever)
- > “Fixed lever long enough, move the world”
ACTUAL DESIGN, NOT JUST ABSTRACT
- > unlike Plato, Pyths, math isn’t otherwordly perfect
- > to be used to shape the world
- > they would say it’s impossible, math too good
- > to be used to shape the world
BREAKS FROM ARISTOTLE, PLATO
- > they thought knowledge for knowledge sake
- > separated techne and episteme
- > first unification of the practical & knowledge
- > learn to make world better through abstract
Death:
- > dies in the Roman siege of Alexandria
- > legend a Praetorian stabbed him on the beach
- > values abstract (circles) > practical (living)
Palimpsest:
- > scroll that’s been written over
- > recently, was revealed the the original text in one was advanced math by Archimedes
- > approaches limits
Eureka!
- > King of Syracuse gold crown, is it real?
- > links bathtub to density
