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Titlebook: Geometry of Continued Fractions; Oleg Karpenkov Textbook 20131st edition Springer-Verlag Berlin Heidelberg 2013 algebraic irrationalities.

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On Integer Geometryhow to find areas of polytopes simply by counting points with integer coordinates contained in them. Finally we formulate one theorem in the spirit of Pick’s theorem: it is the so-called twelve-point theorem.
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Integer Angles of Polygons and Global Relations for Toric Singularitiess of convex polygons. After a brief introduction of the main notions and definitions of complex projective toric surfaces, we discuss two problems related to singular points of toric varieties using integer geometry techniques. As an output one has global relations on toric singularities for toric surfaces.
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