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\(ax^2 + hxy + cy^2 = n\)
John H. Conway
AMS-MAA Joint Lecture Series
1990; 60 minutes; DVD
ISBN-10: 0-8218-4926-3
ISBN-13: 978-0-8218-4926-2
List Price: US$25
Order Code: DVD/33
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With a pictorial approach to the theory of integral quadratic forms, Conway combines an impressive command of the theory with deep intuition to produce an illuminating and engaging lecture. The quadratic forms of the type in the title of this lecture lead to a beautiful picture in the hyperbolic plane--a picture that brings not only understanding of the deeper properties of these forms but also an algorithm for their solution. Taking viewers on a trip down "the river," with a forest of positive integers on one side, and negative integers on the other, Conway shows how this simple representation elucidates certain properties of the forms. His approach also leads to a discussion of a pictorial representation of the real numbers that reveals their Diophantine structure, leading naturally to the concept of the continued fraction representation. This lecture reveals the way this master mathematician wends his intuitive way through the topic, leaving technicalities behind. The DVD would be appropriate for advanced undergraduates with background in number theory.

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