The Theory of the Imaginary in Geometry

The Theory of the Imaginary in Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 232
Release :
ISBN-10 : 9781108013109
ISBN-13 : 1108013104
Rating : 4/5 (09 Downloads)

Synopsis The Theory of the Imaginary in Geometry by : John Leigh Smeathman Hatton

This 1920 publication explores the relationship between real and imaginary non-Euclidean geometry through graphical representations of imaginary geometry.

Geometry of Complex Numbers

Geometry of Complex Numbers
Author :
Publisher : Courier Corporation
Total Pages : 228
Release :
ISBN-10 : 9780486135861
ISBN-13 : 0486135861
Rating : 4/5 (61 Downloads)

Synopsis Geometry of Complex Numbers by : Hans Schwerdtfeger

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Imaginaries in Geometry

Imaginaries in Geometry
Author :
Publisher : Philosophy
Total Pages : 114
Release :
ISBN-10 : 8869773108
ISBN-13 : 9788869773105
Rating : 4/5 (08 Downloads)

Synopsis Imaginaries in Geometry by : Pavel Alexandrovich Florensky

This is the first complete English translation of Pavel Florensky's original and ambitious attempt to arrive at a geometric representation of imaginary numbers, in a context that had already captured the attention of other mathematicians, including Gauss, Argan, Cauchy and Bellavitis. Florensky did not limit his attempt solely to complex projective geometry, but extended it to encompass Ptolemaic-Dantean cosmology and Einstein's Principle of Relativity, as well as a new epistemological theory. The resulting treatise combines various disciplines and explores the relationship between an immanent realm of knowledge and a transcendent one.

Complex Geometry

Complex Geometry
Author :
Publisher : Springer Science & Business Media
Total Pages : 336
Release :
ISBN-10 : 3540212906
ISBN-13 : 9783540212904
Rating : 4/5 (06 Downloads)

Synopsis Complex Geometry by : Daniel Huybrechts

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Author :
Publisher : Springer Science & Business Media
Total Pages : 716
Release :
ISBN-10 : 9780306471223
ISBN-13 : 0306471221
Rating : 4/5 (23 Downloads)

Synopsis New Foundations for Classical Mechanics by : D. Hestenes

(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Dr. Euler's Fabulous Formula

Dr. Euler's Fabulous Formula
Author :
Publisher : Princeton University Press
Total Pages : 416
Release :
ISBN-10 : 9780691175911
ISBN-13 : 0691175918
Rating : 4/5 (11 Downloads)

Synopsis Dr. Euler's Fabulous Formula by : Paul J. Nahin

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Geometric Integration Theory

Geometric Integration Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 344
Release :
ISBN-10 : 9780817646790
ISBN-13 : 0817646795
Rating : 4/5 (90 Downloads)

Synopsis Geometric Integration Theory by : Steven G. Krantz

This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Visual Complex Analysis

Visual Complex Analysis
Author :
Publisher : Oxford University Press
Total Pages : 620
Release :
ISBN-10 : 0198534469
ISBN-13 : 9780198534464
Rating : 4/5 (69 Downloads)

Synopsis Visual Complex Analysis by : Tristan Needham

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Complex Numbers and Geometry

Complex Numbers and Geometry
Author :
Publisher : American Mathematical Soc.
Total Pages : 204
Release :
ISBN-10 : 9781470451820
ISBN-13 : 1470451824
Rating : 4/5 (20 Downloads)

Synopsis Complex Numbers and Geometry by : Liang-shin Hahn

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

Mathematics and the Imagination

Mathematics and the Imagination
Author :
Publisher : Courier Corporation
Total Pages : 402
Release :
ISBN-10 : 9780486320274
ISBN-13 : 0486320278
Rating : 4/5 (74 Downloads)

Synopsis Mathematics and the Imagination by : Edward Kasner

With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.