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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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