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Topic: Proof the irrationality of pi
Replies: 8   Last Post: Sep 10, 2004 10:20 PM

 Messages: [ Previous | Next ]
 Yogi Posts: 323 Registered: 12/6/04
Re: Proof the irrationality of pi
Posted: Sep 9, 2004 9:23 AM

There is a very pretty theorem that says: If c is a positive real
number and there exist a function f(x) that is continuous on [0,c],
positive on (0,c) and such that f and it iterated anti-derivatives can
be taken to be integer valued at 0 and c, then c is irrational!

pi is a positive real number. The function f(x)= sin(x) is
continuous for all x and so on [0,pi] and is positive on (0, pi). All
anti-derivatives can be taken to be +/- sin(x) or +/- cos(x) (by
always choosing the constant of integration to be 0). Therefore
pi is irrational.

Date Subject Author
9/3/04 Farid Ohene Gyan
9/3/04 anonymous
9/3/04 Nat Silver
9/3/04 Peter J. Acklam
9/3/04 anonymous
9/3/04 John Morrison
9/7/04 Julian V. Noble
9/10/04 Julian V. Noble
9/9/04 Yogi