Pythagoras
David Small
Who was Pythagoras
--
Joe Telford
J. B. Stephen (Buck)
In article <bJv5qFAy...@zenecalsm.demon.co.uk>,
Briefly:
Pythagoras was a Greek mathematician, logician, philosopher
and teacher in the classical age of Greece.
Most of what we know about him is hard (or impossible) to
verify. Here is some of what is commonly agreed to:
Pythagoras lived circa 570-500 BCE (aome authors give exact
dates 572-497 BCE).
He is believed to have studied in Egypt and Babylonia before
returning to Greece at about 40 years of age. He settled in
the Greek town of Crotona, which is actually in southern Italy.
Pythagoras appears to be more of a mystical character than a
modern type of rationalist. Part of the Pythagorean philosophy
was a belief in the supremacy of numbers - "number is the
substance of all things".
Aristotle wrote a biography of Pythagoras, but it is lost.
The oldest biography of Pythagoras extant is by Iamblichus,
who wrote almost a thousand years after Pythagoras died. He
was one of the neo-Pythagoreans ( a new group of followers).
Pythagoras is associated with two important mathematical topics:
(1) The Pythagorean Theorem - This is the theorem that says
"the square on the hypotenuse of a right triangle is equal to
the sum of the squares on the legs of the triagle".
This is most certainly not a unique result of Pythagoras, and
it is probable that he learned this relationship from the
Egyptians and Babylonians. This theorem was known before
Pythagoras' time and by many cultures - the oldest reference I
know is to Ancient China.
(2) Incommensurable numbers - This is a little complicated
in its original form, because we think of numbers differently
than the Pythagoreans. The pythagoreans believed that any
two numbers are "comensurable", that is, given two numbers,
there is a third such that both the originals are whole integer
multiples of the third. This is equivalent to the following
more modern statement: given two real numbers a and b, the
fraction a/b is a rational number. Of course, this is not true,
let a=1, and b=square root of 2.
The discovery of incommensurable numbers (and thus irrational real
numbers) is the first crises of mathematics. It forced the Greeks
to rethink their notions of proportion, and took quite some
effort to figure out.
The discovery of incommensurables is traditionally attributed to
Pythaogoras, but it is not believed that Pythagoras, himself,
actually discovered this. There are many stories about the consequences
of this discovery - in one, the follower of Pythagoras who revealed
this fact was thrown overboard and killed. These stories can't
be verified.
Buck
J. Stephen
Dept Math Sci
Northern Illinois University.
SMILEY DAVID WILLIAM
Pythagoras was a presocratic philosopher who pioneered the idea of
metempsychosis or transmigration of the soul, which postulates that the
soul is eternal and that when the body dies the soul flees its former host
and enters into another body human or animal. This belief in
transmigration of the soul is behind Pythagoras' admonition against the
eating of meat. There are no extant writings from Pythagoras per se. But
there are writings ascribed to him by his followers. Look into Diogenes
Laertius book 6 or thereabouts for an ancient biography.
Hope this helps.
David Smiley
U. of Colorado
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(o o)
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cras amet qui numquam amavit |"Let him who has never loved love tomorrow
quique amavit cras amet |and let him who has tomorrow love!
-Pervigilium Veneris
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Lindsay HEYES
Do a web-search for perseus, and you will get a URL for a
searchable database of Greek literature and architecture.
If you search on his name, you should pick up most of what
the Greeks wrote about him.
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% Lindsay Heyes %
% he...@troy.win-uk.net.uk %
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