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

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Working-Memory

Integer Angles of Integer Trianglesgles of an integer triangle; this generalizes the Euclidean condition .+.+.=. for the angles of a triangle (this formula will be used later in Chap. . to study toric singularities). Then we exhibit trigonometric relations for angles of integer triangles. Finally, we give examples of integer triangles with small area.

maudtin

Textbook 20131st edition. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geomet

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Einführung in die Technische Mechaniks 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.

defibrillator

,Gleichgewicht gestützter Körper,xtremely useful for the computation of multidimensional integer invariants of integer objects contained in integer planes). We conclude this chapter with a discussion of the Ehrhart polynomials, which one can consider a multidimensional generalization of Pick’s formula in the plane.

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Kinetik der einfachen Schwinger,s. The first one is a problem of description of empty simplices in dimensions greater than 3. The second is the lonely runner conjecture. We conclude this chapter with a proof of a theorem on the classification of empty tetrahedra.

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,Der thermodynamische Zustand eines Körpers,. After that we discuss homeomorphic and polyhedral structure of the sails in general. Finally we classify all two-dimensional faces with integer distance to the origin greater then one and say a few words about the two-dimensional faces with integer distance to the origin equals one.