Re: PHYS-L digest 914

[Phil Parker <PPARKER@TWSUVM.UC.TWSU.EDU>]

> Date: Mon, 02 Nov 1998 11:33:33 -0600
> From: Gary Karshner <karshner@STMARYTX.EDU>
>
> As pointed out both the diameter and circumference cannot both be
> integers. This is the basis of the classic unsolved problem of Euclidean
> geometry - Squaring the circle, that is construct a square whose area is the
> same that of a circle.
The problem was already solved before Euclid made the Elements, and was
solved again several more times later.  The problem was never solved
*within the constraints* of using only compass and straightedge.  *That*
problem is now *proven* unsolvable using algebraic number theory.  And
that circumference and diameter can't both be integers has nothing to so
with it.  You can construct many irrational numbers with Euclidean
(compass and straightedge) methods.  The problem is to show that pi is
not one of these constructible irrationals.  Now that has a lot to do with
why the mathematically significant thing is not the irrationality of pi,
but its transcendence.

---------------------------------------------
Phil Parker        pparker@twsuvm.uc.twsu.edu
Random quote for this second:
  Humor is laughing at what you haven't got when you ought to
  have it.---Langston Hughes