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RE: Searching for Proof: Three points determine a circle
Posted:
May 7, 2004 2:58 AM
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> -----Original Message-----
> From: owner-geometry-college@mathforum.org [mailto://owner-geometry-
> college@mathforum.org] On Behalf Of Bill Kleinhans
> Sent: Friday, May 07, 2004 12:46 AM
> To: geometry-college@mathforum.org
> Subject: Re: Searching for Proof: Three points determine a circle
>
> On 5 May 04 18:20:59 -0400 (EDT), Paul wrote:
> >I am searching for a formal proof (if there is one).
> >
> >Prove that three non-colinear points determine one and only one
> >circle. None of three points can be the center of the circle.
> >
> >I have searched the web and discovered that Euclid never proved this.
>
Not so. Euclid has this at Book 4, Proposition 5 of his
Elements. See for example
http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV5.html
Note that on the same book Euclid also has (the much harder) problems of
inscribing certain regular polygons into circles.
Have fun.
Michael Lambrou
------- End of Forwarded Message
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