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Brian Lee's sabatic week

🔗TONY SALINAS <salinas@...>

2/27/1997 6:37:23 AM
Dear microtonalists,

I'm writting to anounce that Brian Lee couldn't follow
the discussion on the list about Elssie Hamilton because a major
breakdown on his automated system.

He'll be reading the responses next Monday and getting
back to the list after digestion.

Buen Viaje!!!

Tony Salinas



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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

2/27/1997 10:11:32 AM
PAULE wrote:

''The idea of irrational numbers was too
repugnant to the ancient Greeks''

This is simply a false statement. Pythagoreans were said to have known of
the irrationality of the square root of 2, in the 4th century BC, the
''three big problems'' were solved by Menaechmus and Dinostratus with conic
sections and the quadratrix (a transcendental curve), in the golden age of
Greek Mathematics (3rd century BC), all of the great figures (Archimedes,
Apollonius of Perga, Eratosthenes, Happarchus) used irrationals without
repugnance.

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🔗rtomes@kcbbs.gen.nz (Ray Tomes)

2/27/1997 3:01:22 PM
PAULE wrote:
>''The idea of irrational numbers was too
>repugnant to the ancient Greeks''

Daniel Wolf
>This is simply a false statement. Pythagoreans were said to have known of
>the irrationality of the square root of 2, in the 4th century BC, the
>''three big problems'' were solved by Menaechmus and Dinostratus with conic
>sections and the quadratrix (a transcendental curve), in the golden age of
>Greek Mathematics (3rd century BC), all of the great figures (Archimedes,
>Apollonius of Perga, Eratosthenes, Happarchus) used irrationals without
>repugnance.

Originally the ancient greek mathematics was entirely based on rationals
and they believed that there were no other numbers. I read that the
first guy who proved there were irrationals so upset the applecart that
they took him out to sea and drowned him. The problem was that all
their proofs assumed that only rational numbers existed and so were
completely undermined. Later, they patched it up and were able to cope
with irrationals.

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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