a new look at geometry

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A New Look At Geometry

Author : Irving Adler
ISBN : 9780486320496
Genre : Mathematics
File Size : 29. 19 MB
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This richly detailed overview surveys the evolution of geometrical ideas and the development of the concepts of modern geometry from ancient times to the present. Topics include projective, Euclidean, and non-Euclidean geometry as well as the role of geometry in Newtonian physics, calculus, and relativity. Over 100 exercises with answers. 1966 edition.

To Infinity And Beyond

Author : Eli Maor
ISBN : 9781461253945
Genre : Mathematics
File Size : 44. 85 MB
Format : PDF, ePub
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The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and settled down for the night. But a numbing thought kept him from sleep: How could it be that by merely moving the occupants from one room to another, the first room had become vacated? (Remember, all of the rooms were occupied when he arrived.

Euler Through Time

Author : V. S. Varadarajan
ISBN : 0821835807
Genre : Mathematics
File Size : 55. 48 MB
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Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interest therefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work on elliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5 of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a small number of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).

Methods For Euclidean Geometry

Author : Owen Byer
ISBN : 9780883857632
Genre : Mathematics
File Size : 52. 50 MB
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Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses.

Geometry Its Elements And Structure

Author : Alfred S. Posamentier
ISBN : 9780486492674
Genre : Mathematics
File Size : 86. 47 MB
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"Co-written by a bestselling high school and university textbook author, a longtime educational and standards pioneer, this up-to-date text is geared toward high school geometry classes and contains standard material for numerous state competencies. Topics include plane, solid, coordinate, vector, and non-Euclidean geometry. Features more than 2,000 illustrations, numerous examples with worked-out solutions, and supplementary reading. Electronic solutions manual and annotated teacher's edition are available. "--

A New Approach To Differential Geometry Using Clifford S Geometric Algebra

Author : John Snygg
ISBN : 9780817682828
Genre : Mathematics
File Size : 68. 94 MB
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Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Evolutions In Sustainable Investing

Author : Cary Krosinsky
ISBN : 9781118157923
Genre : Business & Economics
File Size : 80. 58 MB
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Sustainable Investing is fast becoming an essential method of generating long-term returns, moving beyond the negative approaches to socially responsible investing that have dominated the field. This book, our second on the subject, provides over 15 case studies of leading global investors and companies demonstrating how they successfully apply sustainability aspects to their core strategies. Learn from prominent thought leaders Dan Esty and Paul Hawken among others who have contributed key chapters. Our chapter on performance shows clearly how these strategies have been working once negative approaches are parsed out by those examining fund returns. This book also examines in great depth what data exists, and what's on the horizon, to best measure & capture sustainability successfully. Regional perspectives, including 3 chapters on Asia, and focuses on Canada, Australia, Africa & India are also included, as is a look across asset classes. Sustainable Investing, when performed with a positive perspective, has been outperforming the mainstream, unlike negative approaches designed to match benchmark returns. From eco-efficiency to sustainability-driven innovation and beyond, investors of all shapes & sizes need to know how best to position themselves for the radical market shifts underway.

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