Geometry of Continued Fractions

Part 1. Regular continued fractions: Chapter 1. Classical notions and definitions.- Chapter 2. On integer geometry.- Chapter 3. Geometry of regular continued fractions.- Chapter 4. Complete invariant of integer angles.- Chapter 5. Integer trigonometry for integer angles.- Chapter 6. Integer angles of integer triangles.- Chapter 7. Quadratic forms and Makov spectrum..- Chapter 8. Geometric continued fractions.- Chapter 9. Continuant representation of GL(2, Z) Matrices.- Chapter 10. Semigroup of Reduced Matrices.- Chapter 11. Elements of Gauss reduction theory.- Chapter 12. Lagrange's theorem.- Gauss-Kuzmin statistics.- Chapter 14. Geometric aspects of approximation.- Chapter 15. Geometry of continued fractions with real elements and Kepler's second law.- Chapter 16. Extended integer angles and their summation.- Chapter 17. Integer angles of polygons and global relations for toric singularities.- Part II. Multidimensional continued fractions.- Chapter 18. Basic notations and definitions of multidimensional integer geometry.- Chapter 19. On empty simplices, pyramids, parallelepipeds.- Chapter 20. Multidimensional continued fractions in the sense of Klein.- Chapter 21. Dirichlet groups and lattice reduction.- Chapter 22. Periodicity of Klein polyhedral. Generalization of Lagrange's Theorem.- Chapter 23. Multidimensional Gauss-Kuzmin Statistics.- Chapter 24. On the construction of multidimensional continued fractions.- Chapter 25. Gauss reduction in higher dimensions. Chapter 26. Approximation of maximal commutative subgroups.- Capter 27. Other generalizations of continued fractions. References. Index.