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Topic: How to prove that angle in a Circle is 2 Pi Rads ?
Replies: 11   Last Post: Jun 8, 2009 9:23 AM

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Dik T. Winter

Posts: 7,899
Registered: 12/6/04
Re: How to prove that angle in a Circle is 2 Pi Rads ?
Posted: Jun 4, 2009 8:43 PM
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In article <ken.pledger-1BCED6.08381105062009@mara100-84.onlink.net> Ken Pledger <ken.pledger@mcs.vuw.ac.nz> writes:
> In article
> <659af571-e444-4af9-adfd-a0efd8be622b@f10g2000vbf.googlegroups.com>,
> calvin <crice5@windstream.net> wrote:

> > I've often wondered how the ancients were able to
> > find the value of pi so precisely as to know that
> > it is not rational....

>
> AFAIK they didn't. The irrationals in Euclid Book X are all
> algebraic numbers built up from square roots.


They did not know that pi is irrational. The first proof dates from the
18th century. A short proof (requiring not much more than calculus, but
more than the Greek knew about) was found in 1947.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/



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