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Irrationals in Ancient Greece

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

3/1/1997 7:30:05 AM
From: PAULE

>>''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

They made a wide-scale attempt to prevent this fact from becoming known to
the public.

>the
>''three big problems'' were solved by Menaechmus and Dinostratus with conic
>sections and the quadratrix (a transcendental curve)

Yes, and ingenious indeed, in that no irrational quantities were explicitly
used in these constructons!

>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.

What are Aristoxenus' dates?


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