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The article presents some thoughts on making discoveries in present-day Russia. The paper demonstrates how difficult it is for a new and sensible view on the nature of certain matters to reach its audience. In Russia, one must exert oneself to make an impact. The authors argue that a large number of competent ideas and evidence are ignored by the public.

If we replace the V Postulate of Euclid with the Postulate of Lobachevsky, then we can get rectangles with more than 4 angles. The article describes the methodology for constructing such rectangles.

Fermat's Last Theorem has been proved on the basis of school Physics, Mathematics, analytical Geometry. The main conceptions of the proof one can write on a math toy in the form of a wooden cube for children. Six faces of the cube are enough to deliver the main ideas of proof.