Where the truth lies 

 

T.R.- F. Botana 

Proceedings ICCSA (International Conference on Computational Science and its Applications) 2004. Springer. Lec. Not. Com. Sci. 3044, pp. 761-771
 

Consider eight points A, B,..., H such that the following (also eight) triples are collinear  

 

ABD, BCE, CDF, DEG, EFH, FGA, GHB, HAC.  

 

 Then all eight points lie on a line. 

 

"A case study of semialgebraic proving: the Maclane 8_3 theorem"  LNCS 948, Springer,  pp. 183-193 (1995) 

 

• In this paper we consider a semi-automatic proof for a theorem on a configuration of points that is true over the reals but false over the complex field.... 

 

Counterexample 

 

 

"Algebraic and semialgebraic proofs: methods and paradoxes"  

 

• The theorem is intuitively false on the complex field....But if we adhere to our definition of (algebraic) truth, the theorem should be considered true: an example of an obviously false theorem that is  true.