## Day 14: Introduction to Greece;Pythagoreans

### Summary

Background history and geography of Greek civilization. In particular, we need
to understand the place of Greek culture in the genealogy
of Western civilization. There are profound differences in the ways
that Greeks organized their culture in comparison to the ancient
cultures
of Egypt and Mesipotamia. Also, the 'Greece' that is important
for
history of mathematics is different in many ways from the usual
conceptions
of 'Greece'.

Look at maps
from Historical Atlas.

Introduction to Greek mathematics and comparison with ANE and Egypt.

*The Classical Ideal.*

Early Greek mathematics.

Problems of interpretation and evidence.

Pythagorean number theory: special types of numbers; figurate numbers;
theory
of means.

Incommensurability; anthyphareisis.

Music and mathematics.

### Links

Introduction to Greek
civilization

### Reading

B.L. van der Waerden, *Science Awakening*, 92-102.

'Pythagoras of Samos,' DSB.

D.M. Burton *History of Mathematics, *Sections 3.2 and 3.3.

A. Jones, 'Greek Mathematics to AD 300', in I. Grattan-Guinness, *Companion
Encyclopedia of the History and Philosophy of Mathematics*, 46-57.

On to Day 15.

Up to Ancient
and
Classical Mathematics

Last modified: 5 October 2005
Duncan
J.
Melville

Comments to dmelville@stlawu.edu