On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for ... School of the University of Illinois, 1916 - Softcover
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Excerpt from On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Mathematics in the Graduate School of the University of Illinois, 1916
2. The Problem. Since the character of a curve at the infinitely distant noints cannot be studied by the ordinary means at our disposal, several methods have been devised whereby such a study can be made. It is evident at once that,in order to investigate the Singularities at infinity of a curve,the infinite points must be projected to the finite plane. Our problem then consists in the discussion of several methods by which the infinite points of a curve are transformed to the finite nlane and in such a way that the form of the curve at the point in question is preserved. When the character of the curve at the projected infinite point is determined then we have established the character of the singularity at infinity. No essentially new methods are proposed in this paper but the details of the constructions and analytical proofs of.
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Paperback. Condition: New. Print on Demand. This book presents several methods of projective geometry, an advanced study that extends Euclidean concepts to points at infinity, as a solution to examining curve singularities at those points. It is a classic study of a mathematical technique, tracing its origin to foundational Greek geometers over two millennia ago and its continued development throughout history by mathematicians including Newton, Plucker, and Cayley up to the early 20th century. The author presents these methods in great detail, providing historical context, thorough analytical proofs, and visual examples that bring the concepts to life. This book will fascinate those working in curve theory, projective geometry, and the history of mathematics. 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 # 9780282757229_0
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On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Mathematics in the Graduate School of the University of Illinois, 1916
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