Lectures on the Theory of Plane Curves; Delivered to Post-Graduate Students in the University of Calcutta

Lectures on the Theory of Plane Curves; Delivered to Post-Graduate Students in the University of Calcutta
Author: Surendramohan Ganguli
Publisher: Hardpress Publishing
Total Pages: 270
Release: 2012-08-01
Genre:
ISBN: 9781290938617

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Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

LECTURES ON THE THEORY OF PLAN

LECTURES ON THE THEORY OF PLAN
Author: Surendramohan Ganguli
Publisher:
Total Pages: 264
Release: 2016-08-29
Genre: History
ISBN: 9781373677624

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Lectures on the Theory of Plane Curves; Delivered to Post-Graduate Students in the University of Calcutta, Part II

Lectures on the Theory of Plane Curves; Delivered to Post-Graduate Students in the University of Calcutta, Part II
Author: Surendramohan Ganguli
Publisher: Trieste Publishing
Total Pages: 270
Release: 2017-07-27
Genre: History
ISBN: 9780649120451

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Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.

Topological Invariants of Plane Curves and Caustics

Topological Invariants of Plane Curves and Caustics
Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
Total Pages: 70
Release: 1994
Genre: Mathematics
ISBN: 0821803085

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This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.

Lectures on the Theory of Plane Curves, Vol. 2

Lectures on the Theory of Plane Curves, Vol. 2
Author: Surendramohan Ganguli
Publisher: Forgotten Books
Total Pages: 264
Release: 2018-01-13
Genre: Mathematics
ISBN: 9780428976811

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Excerpt from Lectures on the Theory of Plane Curves, Vol. 2: Delivered to Post-Graduate Students in the University of Calcutta The subject of quartic curves is too extensive to be adequately considered in a small work like this. I have therefore confined the discussion chiefly to the most prominent characteristics of these curves. One chapter has been devoted to the consideration of bicircular quartics with special reference to their mode of generation. In fact, this chapter, together with a note in Appendix I, is mainly based on the well-known Memoir on bicircular quartics by Dr. Casey, published in the Transactions of the Royal Irish Academy 1869. Circular cubics have been studied with much advantage, regarded as degenerate bicircular quartics. In the last chapter are considered some well known quartic curves, most of which are bicir cular or are cartesians. A similar consideration, as in the case of cubic curves, has led me to restrict my discourse only to the general properties of these curves. I have intentionally avoided the discussion of Roulettes, Cycloids, etc. Reserving the topics for a future occasion. The reader who desires to study the subject from a higher stand point cau conveniently consult the following works Clebsch - Lecons sur la Geometrie Chasles - Histoire de la Geometrie. In Appendix II, a note on Trinodal Quartics has been inserted. This was communicated to me by Rai A. C. Bose, Bahadur, m.a Controller of Examinations, University of Calcutta. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.