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 "
¥ 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.
GDI