Synopsis
This book delves into the fascinating world of directional calculus, a mathematical system with profound implications for geometry and mechanics. It offers a comprehensive exploration of the methods pioneered by Hermann Grassmann, a visionary mathematician whose work remained largely unrecognized during his time. The author presents a compelling case for the superiority of Grassmann's approach over traditional Cartesian coordinate systems and even Hamilton's quaternions. By emphasizing the inherent geometric dimensions of mathematical quantities, this system provides a more intuitive and elegant framework for understanding complex concepts. Readers will encounter a rich landscape of geometric entities, including points, lines, planes, and vectors, each playing a distinct role in the calculus. The book delves into fundamental operations like addition, subtraction, and multiplication, revealing how these actions interact with geometric objects. As the book progresses, it ventures into applications of directional calculus within plane and solid geometry. Explorations of conics, quadrics, and other geometric figures showcase the power and versatility of this mathematical system. The final chapters extend these principles into the realm of statics, demonstrating how directional calculus can be applied to analyze forces and equilibrium in physical systems. Through its clear explanations and practical examples, this book illuminates the profound elegance and utility of directional calculus, offering readers a deeper appreciation for the underlying structure of geometric space and its applications in various scientific disciplines.
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The Directional Calculus: Based Upon the Methods of Hermann Grassmann
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating world of directional calculus, a mathematical system with profound implications for geometry and mechanics. It offers a comprehensive exploration of the methods pioneered by Hermann Grassmann, a visionary mathematician whose work remained largely unrecognized during his time. The author presents a compelling case for the superiority of Grassmann's approach over traditional Cartesian coordinate systems and even Hamilton's quaternions. By emphasizing the inherent geometric dimensions of mathematical quantities, this system provides a more intuitive and elegant framework for understanding complex concepts. Readers will encounter a rich landscape of geometric entities, including points, lines, planes, and vectors, each playing a distinct role in the calculus. The book delves into fundamental operations like addition, subtraction, and multiplication, revealing how these actions interact with geometric objects. As the book progresses, it ventures into applications of directional calculus within plane and solid geometry. Explorations of conics, quadrics, and other geometric figures showcase the power and versatility of this mathematical system. The final chapters extend these principles into the realm of statics, demonstrating how directional calculus can be applied to analyze forces and equilibrium in physical systems. Through its clear explanations and practical examples, this book illuminates the profound elegance and utility of directional calculus, offering readers a deeper appreciation for the underlying structure of geometric space and its applications in various scientific disciplines. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330367308_0
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The Directional Calculus : Based Upon the Methods of Hermann Grassmann (Classic Reprint)
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