How can I find the proof for the Poncelet-Steiner Theorem?

[sutupidmath]

PONCELET-STEINER Theorem?

Hi everyone,

A friend of mine asked me if i knew of any place where he could find the proof to the Poncelet-Steiner Theorem, so since i knew of none, i thought someone here must know.

The theorem's statement is as follows: All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center.

So, if anyone could tell me a book, a website or something along those lines, where i could find the proof to that theorem i would appreciate it.


All the best!

 

[Condor77]

I recall seeing a proof of this theorem is the following book: Geometric Constructions by George E. Martin.

I sincerely hope this helps.

Regards

 

[sutupidmath]

I recall seeing a proof of this theorem is the following book: Geometric Constructions by George E. Martin.

I sincerely hope this helps.

Regards

Thanks for the refference. This book seems to cost about 45$ in amazon, and if that proof is really there( i am not saying that you are wrong about it) then i'll most probbably purchase that book. So, is there any way that you could confirm for sure that this proof is in that book, so i don't have to spend that money invain(buying a math book is never a waste of money, however i personally don't need that book for the moment so...) ??

Regards!

 

[sutupidmath]

can anyone confirm this, direct me to some other source, or even show a proof here?

 

[Werg22]

Yes, see http://books.google.com/books?id=AB...ontcover&dq=Geometric+Constructions#PPA98,M1".

 

[sutupidmath]

Yes, see http://books.google.com/books?id=AB...ontcover&dq=Geometric+Constructions#PPA98,M1".

Hi Werg22,

Thanks for your input. I have no knowledge of these topics so pardone my ignorance.

I came across that theorem too, but it seems to be different from the one i stated on my first post. Is it just differently worded, or is it a different theorem.

The theorem that my friend is lookig for says:( i am restating it as he emailed it to me)All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center.

Wheras, the theorem that is listed in that book(pg.98) says:

Theorem 6.2(The Poncelet-Steiner Theorem):A point is a ruler and circle point iff the point is a ruler and compas point).


Are these two statements equivalent?

Many thanks!

 

[Werg22]

An entire proof of the statement as you've put it can be found here:

http://books.google.com/books?id=i4...Problems+of+Elementary+Mathematics#PPA165,M1"

The book itself is only $11 USD.

Also there is a proof in College Geometry by Howard Eves, a well-known geometer. The book is discontinued I think, but maybe you can find it at a college library.

 

[sutupidmath]

Thanks a lot guys!

Both of you have been very heplful!