math 5400, history of mathematics - lecture 2: greek ... · some historical remarks what is the di...
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![Page 1: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/1.jpg)
MATH 5400, History of MathematicsLecture 2: Greek Mathematics
Professor: Peter Gibson
http://people.math.yorku.ca/pcgibson/math5400
September 18, 2012
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Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
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Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
![Page 4: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/4.jpg)
Some historical remarks
What is the difference between
Hellenic and
Hellenistic?
P. Gibson (YorkU) Math 5400 18.9.2012 2 / 11
![Page 5: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/5.jpg)
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
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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
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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
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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
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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
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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
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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
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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
![Page 13: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/13.jpg)
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
![Page 14: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/14.jpg)
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
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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
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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
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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
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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
![Page 19: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/19.jpg)
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
![Page 20: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/20.jpg)
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
![Page 21: MATH 5400, History of Mathematics - Lecture 2: Greek ... · Some historical remarks What is the di erence between Hellenic and Hellenistic? P. Gibson (YorkU) Math 5400 18.9.2012 2](https://reader034.vdocuments.mx/reader034/viewer/2022042410/5f2787ad3770f733c46389a4/html5/thumbnails/21.jpg)
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
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Onto the blackboard...
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The dodecahedron:
P. Gibson (YorkU) Math 5400 18.9.2012 9 / 11
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The icosahedron:
P. Gibson (YorkU) Math 5400 18.9.2012 10 / 11
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Some Euclidean geometry...
P. Gibson (YorkU) Math 5400 18.9.2012 11 / 11