Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 151-158 (2000)

Simple Counter Examples for the Unsolvability of the Fermat- and Steiner-Weber-Problem by Compass and Ruler

St. Mehlhos

B.-Brecht-Str. 6, D-07806 Neustadt an der Orla, Germany e-mail:

Abstract: 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 is given a counter example for the construction of the true length of Steiner trees in the three-dimensional space.

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