Playfairs Axiom

Author : Judith Cederberg
Publisher : Springer Science & Business Media
ISBN 13 : 9780387989723
Total Pages : 472 pages
Book Rating : 4.22/5 ( download)

DOWNLOAD NOW!

Download or read book A Course in Modern Geometries written by Judith Cederberg and published by Springer Science & Business Media. This book was released on 2004-09-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".

Author : Henry Sinclair Hall
Publisher :
ISBN 13 :
Total Pages : 286 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book A School Geometry written by Henry Sinclair Hall and published by . This book was released on 1908 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nikolaj Ivanovič Lobačevskij
Publisher : Independently Published
ISBN 13 : 9781099688812
Total Pages : 52 pages
Book Rating : 4.17/5 ( download)

DOWNLOAD NOW!

Download or read book Theory of Parallels written by Nikolaj Ivanovič Lobačevskij and published by Independently Published. This book was released on 2019-05-22 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: LOBACHEVSKY was the first man ever to publish a non-Euclidean geometry. Of the immortal essay now first appearing in English Gauss said, "The author has treated the matter with a master-hand and in the true geometer's spirit. I think I ought to call your attention to this book, whose perusal cannot fail to give you the most vivid pleasure." Clifford says, "It is quite simple, merely Euclid without the vicious assumption, but the way things come out of one another is quite lovely." * * * "What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevsky to Euclid." Says Sylvester, "In Quaternions the example has been given of Algebra released from the yoke of the commutative principle of multiplication - an emancipation somewhat akin to Lobachevsky's of Geometry from Euclid's noted empirical axiom." Cayley says, "It is well known that Euclid's twelfth axiom, even in Playfair's form of it, has been considered as needing demonstration; and that Lobachevsky constructed a perfectly consistent theory, where- in this axiom was assumed not to hold good, or say a system of non- Euclidean plane geometry. There is a like system of non-Euclidean solid geometry." GEORGE BRUCE HALSTED. 2407 San Marcos Street, Austin, Texas. * * * *From the TRANSLATOR'S INTRODUCTION. "Prove all things, hold fast that which is good," does not mean demonstrate everything. From nothing assumed, nothing can be proved. "Geometry without axioms," was a book which went through several editions, and still has historical value. But now a volume with such a title would, without opening it, be set down as simply the work of a paradoxer. The set of axioms far the most influential in the intellectual history of the world was put together in Egypt; but really it owed nothing to the Egyptian race, drew nothing from the boasted lore of Egypt's priests. The Papyrus of the Rhind, belonging to the British Museum, but given to the world by the erudition of a German Egyptologist, Eisenlohr, and a German historian of mathematics, Cantor, gives us more knowledge of the state of mathematics in ancient Egypt than all else previously accessible to the modern world. Its whole testimony con- firms with overwhelming force the position that Geometry as a science, strict and self-conscious deductive reasoning, was created by the subtle intellect of the same race whose bloom in art still overawes us in the Venus of Milo, the Apollo Belvidere, the Laocoon. In a geometry occur the most noted set of axioms, the geometry of Euclid, a pure Greek, professor at the University of Alexandria. Not only at its very birth did this typical product of the Greek genius assume sway as ruler in the pure sciences, not only does its first efflorescence carry us through the splendid days of Theon and Hypatia, but unlike the latter, fanatics cannot murder it; that dismal flood, the dark ages, cannot drown it. Like the phoenix of its native Egypt, it rises with the new birth of culture. An Anglo-Saxon, Adelard of Bath, finds it clothed in Arabic vestments in the land of the Alhambra. Then clothed in Latin, it and the new-born printing press confer honor on each other. Finally back again in its original Greek, it is published first in queenly Basel, then in stately Oxford. The latest edition in Greek is from Leipsic's learned presses.

Author : Hongyu Guo
Publisher : World Scientific Publishing Company
ISBN 13 : 9814449350
Total Pages : 524 pages
Book Rating : 4.59/5 ( download)

DOWNLOAD NOW!

Download or read book Modern Mathematics And Applications In Computer Graphics And Vision written by Hongyu Guo and published by World Scientific Publishing Company. This book was released on 2014-04-01 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.

Author : Gerolamo Saccheri
Publisher : Springer
ISBN 13 : 3319059661
Total Pages : 384 pages
Book Rating : 4.62/5 ( download)

DOWNLOAD NOW!

Download or read book Euclid Vindicated from Every Blemish written by Gerolamo Saccheri and published by Springer. This book was released on 2014-08-07 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work. Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the time. In particular, the Parallel Postulate had escaped demonstration since the first attempts at it in the Classical Age, and several books on the topic were published in the Early Modern Age. At the same time, the theory of proportion was the most important mathematical tool of the Galilean School in its pursuit of the mathematization of nature. Saccheri's attempt to prove the Parallel Postulate is today considered the most important breakthrough in geometry in the 18th century, as he was able to develop for hundreds of pages and dozens of theorems a system in geometry that denied the truth of the postulate (in the attempt to find a contradiction). This can be regarded as the first system of non-Euclidean geometry. Its later developments by Lambert, Bolyai, Lobachevsky and Gauss eventually opened the way to contemporary geometry. Occupying a unique position in the literature of mathematical history, Euclid Vindicated from Every Blemish will be of high interest to historians of mathematics as well as historians of philosophy interested in the development of non-Euclidean geometries.

Author : Saraswati Experts
Publisher : New Saraswati House India Pvt Ltd
ISBN 13 : 9350412640
Total Pages : pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Me n Mine-Mathematics- Term-1 written by Saraswati Experts and published by New Saraswati House India Pvt Ltd. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A text book on Maths

Author : Francis Bacon
Publisher :
ISBN 13 :
Total Pages : 426 pages
Book Rating : 4.HM/5 ( download)

DOWNLOAD NOW!

Download or read book The Advancement of Learning written by Francis Bacon and published by . This book was released on 1895 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : David Hilbert
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.15/5 ( download)

DOWNLOAD NOW!

Download or read book The Foundations of Geometry written by David Hilbert and published by . This book was released on 1910 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Victor J. Katz
Publisher :
ISBN 13 : 9780134689524
Total Pages : 0 pages
Book Rating : 4.26/5 ( download)

DOWNLOAD NOW!

Download or read book A History of Mathematics written by Victor J. Katz and published by . This book was released on 2017-03-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. A History of Mathematics, 3rd Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today's elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic.

Author : James Martin Peebles
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.53/5 ( download)

DOWNLOAD NOW!

Download or read book Vaccination a Curse and a Menace to Personal Liberty written by James Martin Peebles and published by . This book was released on 1913 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: