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Synopsis
From the Proceedings of theL ondon Mathematical Society, vol. v. (1873 1874), pp. 14 25. Read December 11, 1873.] I HAVE constructed a model and drawings of the symmetrical form of Steiner sS urface, viz. that wherein the four singular tangent planes form a regular tetrahedron, and consequently the three nodal lines (being the lines joining the mid-points of opposite edges) a system of rectangular axes at the centre of the tetrahedron. Before going into the analytical theory, I describe as follows the general form of the surface: take the tetrahedron, and inscribe in each face a circle (there will be, of course, two circles touching at the mid-point of each edge of the tetrahedron; each circle will contain, on its circumference at angular distances of 120 ,three mid-points, and the lines joining these with the centre of the tetrahedron, produced beyond the centre, meet the opposite edges, and are in fact the before-mentioned lines joining the midpoints of opposite edges). Now truncate the tetrahedron by planes parallel to the faces so as to reduce the altitudes each to three-fourths of the original value, and from the centre of each new face round off symmetrically up to the adjacent three circles; and within each circle scoop down to the centre of the tetrahedron, the bounding surface of the excavation passing through the three right lines, and the sections (by planes parallel to the face) being in the neighbourhood of the face nearly circular, but as they approach the centre, assuming a trigonoidal form, and being close to the centre an indefinitely small equilateral triangle. We have thus the surface, consisting of four lobes united only by the lines through the mid-points of opposite edges, these lines being consequently nodal lines; the mid-points being pinch-points of the surface, and the faces singular planes, each touching the surface along the inscr
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- PublisherForgotten Books
- Publication date2024
- ISBN 10 1440044937
- ISBN 13 9781440044939
- BindingPaperback
- Number of pages644
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The Collected Mathematical Papers of Arthur Cayley, Vol. 9 (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book is the result of the author's lifelong interest in the mathematical theory of functions and the development of ideas in the field during the nineteenth century. The book explores the works of some of the most prominent mathematicians of the period, including Gauss, Jacobi, Abel, and Riemann, and shows how their ideas led gradually to the formulation of a theory of functions that is based on Cauchy's theory of residues. This permits the author to link, in a comprehensive and detailed manner, various aspects of the subject together and to provide a coherent account of its development. Even today, this book is very useful for mathematicians, scientists, and engineers whose research is connected with the theory of functions. Forgotten Books publishes hundreds of thousands of rare and classic books. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Seller Inventory # 9781440044939_0
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The Collected Mathematical Papers of Arthur Cayley, Vol 9 Classic Reprint
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The Collected Mathematical Papers of Arthur Cayley, Vol. 9 of 13 (Classic Reprint)
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Paperback. Condition: Brand New. 644 pages. 9.02x5.98x1.46 inches. This item is printed on demand. Seller Inventory # zk1440044937
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