Dear all,

I have attempted to make a poem on famous Thebault�s problem and

it�s solution given by various geometers over the period.My English is not

good,so please bear with this.

Also please supply me the details if any more geometers that

have published it�s solution.I think Dr.John Rigby has solved Thebault�s

problem in his paper "Tritangent centers,Pascal�s theorem and Thebault�s

problem - Journal of Geometry 54 (1995) , no. 1-2 , 134-147 ".I don�t have

the paper with me.If anybody tells me then I�ll surely append their name

too.

THEBAULT�S PROBLEM

For forty-five years remained unsolved,

The problem proposed by Victor Thebault;

A prolific geometer from France

Who posed it to geometry fans,

Concerning collinear centers three,

2 of circles touching cevian arbitrary

and also the base and circumcircle;

the third one of the incircle

Tried and tried but people in vain

Thebault�s problem gained ebullient fame

No solution arrived at thee

Until the year came 1983,

Where K.B.Taylor gave a solution,

Based upon a lengthy calculation

24 pages it occupied totally,

but only summary appeared in the Monthly.

Later came G.Turnwald,

Reduced the length of the problem he solved,

Now it was the turn of Swarnendu Dutta

A young school boy from Calcutta,

Solved the problem completely,

No trigonometry only synthetically!

Then Ron Shail in 2001 Monthly,

Gave another solution analytically.

So exhilarating has been the journey of this sum

In Honsberger�s term a GREAT mathematical plum,

Thus for this geometric gem as well as emerald,

Hats off to VICTOR THEBAULT!!!

I hope you didn�t get bored.Any suggestions are gratefully welcome.

Yours faithfully

Atul.A.Dixit

_________________________________________________________________

Chat with friends online, try MSN Messenger:

http://messenger.msn.com