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Application Of Geometry To Imaginaries And To Imaginary Roots Of Equations
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Book Synopsis Application of Geometry to Imaginaries and to Imaginary Roots of Equations ... by : Herrick Ernest Herbert Greenleaf
Download or read book Application of Geometry to Imaginaries and to Imaginary Roots of Equations ... written by Herrick Ernest Herbert Greenleaf and published by . This book was released on 1925 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Graphs and Imaginaries by : J. G. Hamilton
Download or read book Graphs and Imaginaries written by J. G. Hamilton and published by . This book was released on 1904 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Graphs and Imaginaries by : J. G. Hamilton
Download or read book Graphs and Imaginaries written by J. G. Hamilton and published by Forgotten Books. This book was released on 2017-11-27 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Graphs and Imaginaries: An Easy Method of Finding Graphically Imaginary Roots of Quadratic Equations and Imaginary Points of Intersections of Various Curves; With Illustrations of the Principle From Elementary Geometry N the following pages we develop a method by which imaginary roots of a quadratic equation can be found. 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.
Book Synopsis Graphs and Imaginaries by : J G Hamilton
Download or read book Graphs and Imaginaries written by J G Hamilton and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover a new method for finding imaginary roots of quadratic equations and the points of intersection of various curves with this innovative text by J. G. Hamilton. Through the use of simple graphical techniques, Hamilton demonstrates how complex mathematical concepts can be easily understood and applied. Perfect for mathematicians, scientists, or anyone seeking a new perspective on the world of mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis GRAPHS & IMAGINARIES AN EASY M by : F. Kettle
Download or read book GRAPHS & IMAGINARIES AN EASY M written by F. Kettle and published by Wentworth Press. This book was released on 2016-08-26 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis The Theory of the Imaginary in Geometry by : J. Hatton
Download or read book The Theory of the Imaginary in Geometry written by J. Hatton and published by CreateSpace. This book was released on 2015-07-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE word theory in the title is to be understood in a very non-technical sense. Indeed, apart from the idea of the invariant elements of an elliptic involution on a straight line, no theory is found at all. The purpose of the book is rather to furnish a certain graphical representation of imaginaries under a number of conventions more or less well known. Three concepts run through the work: first, an incompletely defined idea of the nature of an imaginary; second, the analogy with the geometry of reals; third, the use of coordinate methods, assuming the algebra of imaginaries. Given a real point O and a real constant k, an imaginary point P is defined by the equation OP2 = -k - 2. The two imaginary points P and P' are the double points of an involution having O for center, and ik for parameter. The algebra of imaginaries is now assumed, and a geometry of imaginary distances on a straight line is built upon it. The reader is repeatedly reminded that in themselves there is no difference between real and imaginary points; that differences exist solely in their relations to other points. In the extension to two dimensions both x and ix are plotted on a horizontal line, while x and xy are plotted on a vertical line. Imaginary lines are dotted, and points having one or both coordinates imaginary are enclosed by parentheses, but otherwise the same figures are used for proofs, either by the methods of elementary geometry, or by coordinate methods.In the algebra of segments it is shown that an imaginary distance O'D' can be expressed in the form iOD, wherein OD is a real segment, or at most by OD times some number. Now follows a long development of the extension of cross ratios, etc., to imaginaries. In fact every word of this is found implicitly in any treatment of the invariance of cross ratios under linear fractional transformation.In Chapter II the conic with a real branch is introduced, beginning with involutions of conjugate points on lines having imaginary points on the conic. If the coefficients in the equation of a circle are real, the usual graph of x2 + y2 = a2 for real x and real y is followed by replacing y by iy, then proceeding as before. The former locus is called the (1, 1) branch, and the latter the (1, i) branch of the circle. Similarly, it has a (i, 1) branch, and another, (i, i) , but the latter has no graph. This idea is applied in all detail to ellipses, hyperbolas, and parabolas; in the case of the central conies it is also followed by replacing rectangular coordinates by a pair of conjugate diameters. The ordinary theorems of poles and polars, and the theorems of Pascal, Brianchon, Desargues, Carnot are shown to apply. Indeed, after having established the applicability of cross ratios in the earlier chapters, all these proofs can be applied in the same manner as to reals, without changing a word....-An excerpt from Bulletin of the American Mathematical Society, Vol. 27 [1921]
Book Synopsis Euclidean Geometry and Transformations by : Clayton W. Dodge
Download or read book Euclidean Geometry and Transformations written by Clayton W. Dodge and published by Courier Corporation. This book was released on 2012-04-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Book Synopsis Algebra identified with Geometry; that is to say, ordinary ... algebra ... shewn to be a purely geometrical ... calculus, etc by : Alexander John ELLIS
Download or read book Algebra identified with Geometry; that is to say, ordinary ... algebra ... shewn to be a purely geometrical ... calculus, etc written by Alexander John ELLIS and published by . This book was released on 1874 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Redefining Geometrical Exactness by : Henk J.M. Bos
Download or read book Redefining Geometrical Exactness written by Henk J.M. Bos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. He then analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness.
Book Synopsis Algebra Identified with Geometry ... by : Alexander John Ellis
Download or read book Algebra Identified with Geometry ... written by Alexander John Ellis and published by . This book was released on 1874 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Geometry of Position by : Theodor Reye
Download or read book Lectures on the Geometry of Position written by Theodor Reye and published by . This book was released on 1898 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry by : Scott
Download or read book An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry written by Scott and published by . This book was released on 1894 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Analytic and Projective Geometry by : Dirk J. Struik
Download or read book Lectures on Analytic and Projective Geometry written by Dirk J. Struik and published by Courier Corporation. This book was released on 2014-03-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
Book Synopsis An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry by : Charlotte Angas Scott
Download or read book An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry written by Charlotte Angas Scott and published by . This book was released on 1894 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions by : Charles Briot
Download or read book Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions written by Charles Briot and published by . This book was released on 1896 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Indiana Academy of Science by : Indiana Academy of Science
Download or read book Proceedings of the Indiana Academy of Science written by Indiana Academy of Science and published by . This book was released on 1891 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: List of members in each volume.
Download or read book An Imaginary Tale written by Paul Nahin and published by Princeton University Press. This book was released on 2010-02-22 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
