MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di...
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MATH 5400, History of Mathematics Lecture 2: Greek Mathematics Professor: Peter Gibson [email protected] http://people.math.yorku.ca/pcgibson/math5400 September 18, 2012
Transcript of MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di...
MATH 5400, History of MathematicsLecture 2: Greek Mathematics
Professor: Peter Gibson
http://people.math.yorku.ca/pcgibson/math5400
September 18, 2012
Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
The Dark Ages (1100-800BC), The Golden Age of Greece (∼ 500-300BC)
Homer is alleged to have lived c. 750BC
Pythagorus lived c. 530BC, founding a religious community in Croton
The Peleponnesian War took place 431-404BC
P. Gibson (YorkU) Math 5400 18.9.2012 3 / 11
The Dark Ages (1100-800BC), The Golden Age of Greece (∼ 500-300BC)
Homer is alleged to have lived c. 750BC
Pythagorus lived c. 530BC, founding a religious community in Croton
The Peleponnesian War took place 431-404BC
P. Gibson (YorkU) Math 5400 18.9.2012 3 / 11
The Dark Ages (1100-800BC), The Golden Age of Greece (∼ 500-300BC)
Homer is alleged to have lived c. 750BC
Pythagorus lived c. 530BC, founding a religious community in Croton
The Peleponnesian War took place 431-404BC
P. Gibson (YorkU) Math 5400 18.9.2012 3 / 11
The Dark Ages (1100-800BC), The Golden Age of Greece (∼ 500-300BC)
Homer is alleged to have lived c. 750BC
Pythagorus lived c. 530BC, founding a religious community in Croton
The Peleponnesian War took place 431-404BC
P. Gibson (YorkU) Math 5400 18.9.2012 3 / 11
The Peleponnesian War undermined the political institutions of the day,although high culture continued to flourish...
A famous succession of Golden age scholars:
Socrates (469-399BC)
Plato (427-347BC)
Aristotle (384-322BC)
P. Gibson (YorkU) Math 5400 18.9.2012 4 / 11
The Peleponnesian War undermined the political institutions of the day,although high culture continued to flourish...
A famous succession of Golden age scholars:
Socrates (469-399BC)
Plato (427-347BC)
Aristotle (384-322BC)
P. Gibson (YorkU) Math 5400 18.9.2012 4 / 11
The Peleponnesian War undermined the political institutions of the day,although high culture continued to flourish...
A famous succession of Golden age scholars:
Socrates (469-399BC)
Plato (427-347BC)
Aristotle (384-322BC)
P. Gibson (YorkU) Math 5400 18.9.2012 4 / 11
The Peleponnesian War undermined the political institutions of the day,although high culture continued to flourish...
A famous succession of Golden age scholars:
Socrates (469-399BC)
Plato (427-347BC)
Aristotle (384-322BC)
P. Gibson (YorkU) Math 5400 18.9.2012 4 / 11
The Peleponnesian War undermined the political institutions of the day,although high culture continued to flourish...
A famous succession of Golden age scholars:
Socrates (469-399BC)
Plato (427-347BC)
Aristotle (384-322BC)
P. Gibson (YorkU) Math 5400 18.9.2012 4 / 11
The political authority was fragile, however, and in 338BC Philip ofMacedon conquered much of Greece.
His son, Alexander, succeeded him in 336BC.
P. Gibson (YorkU) Math 5400 18.9.2012 5 / 11
The political authority was fragile, however, and in 338BC Philip ofMacedon conquered much of Greece.
His son, Alexander, succeeded him in 336BC.
P. Gibson (YorkU) Math 5400 18.9.2012 5 / 11
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals,
leading to the Hellenistic period.
Two very prominent mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
P. Gibson (YorkU) Math 5400 18.9.2012 6 / 11
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Two very prominent mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
P. Gibson (YorkU) Math 5400 18.9.2012 6 / 11
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Two very prominent mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
P. Gibson (YorkU) Math 5400 18.9.2012 6 / 11
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Two very prominent mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
P. Gibson (YorkU) Math 5400 18.9.2012 6 / 11
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Two very prominent mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
P. Gibson (YorkU) Math 5400 18.9.2012 6 / 11
Some Mathematics
Definition
A platonic solid, is a convex regular polyhedron with the followingproperties:
Each face is a regular polygon.
All faces are congruent to one another.
Each vertex meets the same number of edges as every other vertex.
P. Gibson (YorkU) Math 5400 18.9.2012 7 / 11
Onto the blackboard...
P. Gibson (YorkU) Math 5400 18.9.2012 8 / 11
The dodecahedron:
P. Gibson (YorkU) Math 5400 18.9.2012 9 / 11
The icosahedron:
P. Gibson (YorkU) Math 5400 18.9.2012 10 / 11
Some Euclidean geometry...
P. Gibson (YorkU) Math 5400 18.9.2012 11 / 11
