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Excerpt from Elements of Quaternions, Vol. 2
In other words, the calculation of 1' and P introduces no differentials higher than the third order but that of R' requires the fourth order of differentials. In the language of modern geometry, the former can be determined by the consideration of four consecutive points of the curve, or by that of two consecutive osculating circles; but the latter requires the consideration of two consecutive osculating spheres, and therefore of five consecutive points of the curve (supposed to be one of double curvature). Other investigations, in the present and immediately following Series (398.
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Elements of Quaternions, Vol. 2 (Classic Reprint)
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Elements of Quaternions, Vol. 2 (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book delves into the fascinating world of quaternions, a mathematical concept developed by the Irish mathematician William Rowan Hamilton in the mid-19th century. Quaternions extend the familiar system of complex numbers to three-dimensional space, offering a powerful tool for representing and manipulating geometric objects and relationships. The author explores the applications of quaternions in diverse areas of geometry, including the study of curves in space, surfaces of the second order, and lines of curvature. He examines concepts like osculating circles and spheres, geodetic lines, and the unique properties of umbilics on central quadrics. Through a combination of rigorous analysis and insightful explanations, the book illuminates the elegance and depth of quaternion methods. It reveals how this mathematical tool can be used to express and derive complex geometric theorems in a concise and elegant manner. This book offers a valuable resource for anyone seeking a deeper understanding of the power and beauty of quaternion mathematics, and its implications for various branches of geometry. 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. Codice articolo 9781330441169_0
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