Re: Pi day

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#83

From: Kathrin Paschen
Date: Fri, 21 Mar 1997 00:00

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Mark Gibson (mgibson@vcn.bc.ca) wrote:

: Incidentelly I'm sure it must have ocurred to someone that there are
: DEGREES of irrationality among the irrational numbers. For axample some
: irrational numbers when subjected to a simple operation can be mapped to a
: rational number. e.g. sqrt(2)*sqrt(2) = 2. Whilst as far as I know e*e and
: pi*pi, e*pi, etc are still irrational. Since this ocurred to a
: mathematical dunce like me it can't be that important but I though it was
: interesting, so there.

That's because pi and e are transcendental, while sqrt(2) is algebraic.
Transcendental numbers cannot solve a rational polynomial (they cannot
be 'mapped to a rational number' the way you did with sqrt(2)).
All rational numbers are algebraic, but not all irrational ones are.
It's a very fascinating subject :).

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From: s_pasche@ira.uka.de (Kathrin Paschen)
Subject: Re: Pi day
Date: 1997/03/21
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Organization: University of Karlsruhe, Germany
Newsgroups: uk.education.maths,alt.uu.math.misc,aus.mathematics,can.schoolnet.math.sr,alt.math.recreational,sci.math

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