Simple counter examples for the unsolvability of the Fermat- and Steiner- Weber- problem by compass and ruler. (English)

Beitr. Algebra Geom. 41, No. 1, 151-158 (2000).

The purpose of this short note is to give counter examples for the unsolvability of the Fermat- and Steiner-Weber-problem by compass and ruler. The used point sets made it possible to obtain for the Fermat-problem polynomials of the degree 3 and 4. Thus, for these counter examples Galois theory and computer algebra is not necessary. In the second part a counter example is given for the construction of the true length of Steiner trees in the three-dimensional space. (Orig.)