Non-Euclidean Geometry for Babies


Author: Fred Carlson
Publisher: Createspace Independent Pub
ISBN: 9781480203242
Category: Mathematics
Page: 34
View: 5516

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This survey of topics in Non-Euclidean Geometry is chock-full of colorful diagrams sure to delight mathematically inclined babies. Non-Euclidean Geometry for Babies is intended to introduce babies to the basics of Euclid's Geometry, and supposes that the so-called "Parallel Postulate" might not be true. Mathematician Fred Carlson believes that it's never too early to introduce children, and even babies, to the basic concepts of advanced mathematics. He is sure that after reading this book, the first in his Mathematics for Babies series, you will agree with him! This is one of two versions of this title. The interior of both books is identical, but the cover design on this one is done in Pretty Pink, perfect for babies who prefer the color pink instead of blue. The Baby Blue edition can be found here: http://www.amazon.com/dp/1481050044

Non-Euclidean Geometry


Author: H. S. M. Coxeter
Publisher: Cambridge University Press
ISBN: 9780883855225
Category: Mathematics
Page: 336
View: 4243

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A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.

Introduction to Hyperbolic Geometry


Author: Arlan Ramsay,Robert D. Richtmyer
Publisher: Springer Science & Business Media
ISBN: 1475755856
Category: Mathematics
Page: 289
View: 4942

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This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

Introductory Non-Euclidean Geometry


Author: Henry Parker Manning
Publisher: Courier Corporation
ISBN: 0486154645
Category: Mathematics
Page: 112
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This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.

Sources of Hyperbolic Geometry


Author: John Stillwell
Publisher: American Mathematical Soc.
ISBN: 9780821809228
Category: Mathematics
Page: 153
View: 7076

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This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue--not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincare brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Poincare in their full brilliance.

Geometry: Euclid and Beyond


Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 0387226761
Category: Mathematics
Page: 528
View: 4261

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This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Geometry of Lengths, Areas, and Volumes: Two-Dimensional Spaces, Volume 1


Author: James W. Cannon
Publisher: American Mathematical Soc.
ISBN: 1470437147
Category: Geometry
Page: 119
View: 936

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This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.

Euclidean Geometry in Mathematical Olympiads


Author: Evan Chen
Publisher: The Mathematical Association of America
ISBN: 0883858398
Category: Mathematics
Page: 311
View: 8702

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This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.

Lectures on Hyperbolic Geometry


Author: Riccardo Benedetti,Carlo Petronio
Publisher: Springer Science & Business Media
ISBN: 3642581587
Category: Mathematics
Page: 330
View: 8858

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Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.

Foundations of Hyperbolic Manifolds


Author: John Ratcliffe
Publisher: Springer Science & Business Media
ISBN: 1475740131
Category: Mathematics
Page: 750
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This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Introduction To Non-Euclidean Geometry


Author: Harold E. Wolfe
Publisher: Read Books Ltd
ISBN: 1446547302
Category: Science
Page: 260
View: 9119

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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Introduction to Projective Geometry


Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486141705
Category: Mathematics
Page: 576
View: 5509

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This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.

A History of Non-Euclidean Geometry

Evolution of the Concept of a Geometric Space
Author: Boris A. Rosenfeld
Publisher: Springer Science & Business Media
ISBN: 1441986804
Category: Mathematics
Page: 471
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The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

Euclidean and Non-euclidean Geometries


Author: Maria Helena Noronha
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 409
View: 398

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Designed for undergraduate juniors and seniors, Noronha's (California State U., Northridge) clear, no-nonsense text provides a complete treatment of classical Euclidean geometry using axiomatic and analytic methods, with detailed proofs provided throughout. Non-Euclidean geometries are presented usi

The Pythagorean Theorem for Babies


Author: Fred Carlson
Publisher: Createspace Independent Pub
ISBN: 9781482000580
Category: Mathematics
Page: 28
View: 4790

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The Pythagorean Theorem for Babies is intended to introduce babies to the principles of the Pythagorean Theorem, and also provides a colorful proof of the theorem. Mathematician Fred Carlson believes that it's never too early to introduce children, and even babies, to the basic concepts of advanced mathematics. He is sure that after reading this book, the second in his Mathematics for Babies series, you will agree with him! If you like this book, please also check out "Non-Euclidean Geometry for Babies"!

Lessons in Geometry: Plane geometry


Author: Jacques Hadamard
Publisher: American Mathematical Soc.
ISBN: 0821843672
Category: Mathematics
Page: 330
View: 5499

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This is a work in the tradition of Euclidean synthetic geometry written by one of the 20th century's great mathematicians. The text starts where Euclid starts, and covers all the basics of plane Euclidean geometry.

Ideas of Space

Euclidean, Non-Euclidean, and Relativistic
Author: Jeremy Gray
Publisher: Oxford University Press
ISBN: 0198539355
Category: Mathematics
Page: 242
View: 8709

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Ideas of Space is a lively and readable account of the development of Euclidean, non-Euclidean, and relativistic ideas of the shape of the universe. For this new edition the author has updated much of the material and added a chapter on the emerging story of the Arabic contribution.