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Titlebook: Geometry Through History; Euclidean, Hyperboli Meighan I. Dillon Textbook 2018 Springer International Publishing AG, part of Springer Natur

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Textbook 2018t assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field..
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Neutral Geometry,f a struggle, the problem of the parallels seemed an intractable monster, devouring egos, relationships, and careers, threatening to destabilize mathematics itself. Yet in retrospect, the struggle was so fruitful and its resolution so startling that the problem itself seems a gift.
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Algebraic Curves,confine our attention to algebraic plane curves, that is, curves given by the zero sets associated to polynomials over . in two variables. Our goal is to appreciate Bézout’s Theorem for plane curves, one of the cornerstones of the subject.
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,Das System der doppelten Buchführung,s naturally associated to triangles, typifies work done in Euclidean geometry in Europe during the eighteenth and nineteenth centuries. With circular inversion and the nine point circle as goals, our journey winds naturally through some favorite classical ideas in Euclidean geometry.
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The Elements of Euclid,bjects of study. In differential geometry, for example, the objects are curves and surfaces in complex space and the tools arise largely from differential calculus. Algebraic geometry is the study of objects that can be described using rational functions and the tools arise typically, but not always, from modern algebra.
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