Quadratic Irrationals

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Focusing on the unification of various aspects of number theory, this book explores continued fractions, quadratic orders, binary quadratic forms, and class groups through the lens of quadratic irrationals. It bridges classical and contemporary results, emphasizing the relationship between Gauss's theory of binary forms and the arithmetic of quadratic orders. By addressing the disorganization in the literature and the lack of standardized notation, it provides a cohesive framework for understanding these mathematical concepts.