Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed superb by teachers who have used the text.

A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight intothe subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

Miranda Lundy gives us a beautiful glimpse into the world of shapes and the geometry behind some of mankind's most famous creations.

Geometry is one of a group of special sciences - Number, Music and Cosmology are the others - found identically in nearly every culture on earth. In this small volume, Miranda Lundy presents a unique introduction to this most ancient and timeless of universal sciences.

Sacred Geometry demonstrates what happens to space in two dimensions - a subject last flowering in the art, science and architecture of the Renaissance and seen in the designs of Stonehenge, mosque decorations and church windows. With exquisite hand-drawn images throughout showing the relationship between shapes, the patterns of coin circles, and the definition of the golden section, it will forever alter the way in which you look at a triangle, hexagon, arch, or spiral.

Wooden Books was founded in 1999 by designer John Martineau near Hay-on-Wye. The aim was to produce a beautiful series of recycled books based on the classical philosophies, arts and sciences. Using the Beatrix Potter formula of text facing picture pages, and old-styles fonts, along with hand-drawn illustrations and 19th century engravings, the books are designed not to date. Small but stuffed with information. Eco friendly and educational. Big ideas in a tiny space. There are over 1,000,000 Wooden Books now in print worldwide and growing.

This concise text introduces students to the elements of analytical geometry, covering basic ideas and methods. Topics include transformation of axes, the line at infinity, conics and pencils of conics, homographic correspondence, line-coordinates, and generalized homogeneous coordinates. An appendix discusses solutions to many of the examples. 1957 edition.

From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the twentieth century, and explores the wide range of applications in science, and in aspects of economics.

About the Series:
Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can see geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships.

We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry.

Specifically designed as an integrated survey of the development of analytic geometry, this classic study takes a unique approach to the history of ideas. The author, a distinguished historian of mathematics, presents a detailed view of not only the concepts themselves, but also the ways in which they extended the work of each generation, from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the Golden Age, from 1789 to 1850. Appropriate as an undergraduate text, this history is accessible to any mathematically inclined reader. 1956 edition. Analytical bibliography. Index.

Illustrated with interesting examples from everyday life, this text shows how to create ellipses, parabolas, and hyperbolas and presents fascinating historical background on their ancient origins. The text starts with a discussion of techniques for generating the conic curves, showing how to create accurate depictions of large or small conic curves and describing their reflective properties, from light in telescopes to sound in microphones and amplifiers. It further defines the role of curves in the construction of auditoriums, antennas, lamps, and numerous other design applications. Only a basic knowledge of plane geometry needed; suitable for undergraduate courses. 1993 edition. 98 figures.

This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space.
Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of road signs in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problems -- with solutions, answers, and hints -- promote habits of independent work

Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students.
Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geometry, geometry on the sphere, and reduction of real matrices to diagonal form. Exercises appear throughout the text, with complete answers at the end.

A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. It makes extensive use of determinants, but no previous knowledge is assumed; they are introduced from the beginning as a natural tool for coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed and carried farther than is usual in algebra courses. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises throughout the text incorporate -- often in rather novel settings -- each idea after its full and careful explanation. 1939 edition.

Geometry is heavy in definitions, theorems, and proofs. If you are struggling to keep it all straight and don't have time for hundreds of pages of math speak, you will love this book The NOW 2 kNOW(TM) Geometry text concisely organizes the subject's vast amount of information and provides numerous examples of proofs as well as over 200 problems with worked out solutions. Inside this book: -Lines, Angles, Planes -Logic & Truth Tables -Triangles, Polygons, Circles, Solids -Congruency & Similitude -Transformations with Coordinates -Locus & Concurrency -Introduction to Trigonometry

Euclid's masterpiece textbook, The Elements, was written twenty-three hundred years ago. It is primarily about geometry and contains dozens of figures. Five of these are constructed using a line that is cut in extreme and mean ratio. Today this is called the golden ratio and is often referred to by the symbol Φ.

Many myths have grown up around this ratio. This book was written to learn about them. They arise from the pyramids, the Pythagorean Brotherhood, the platonic solids, the Fibonacci numbers, sea shells, and others. There is a common thread among these myths. Φ is an irrational number (a number whose digits after the decimal point go on forever and never form a repeating pattern). Φ can be used to draw pleasing figures. But its numerical value cannot be written down using integers and fractions, which were the only numbers used in Euclid's time.

Mathematicians before Euclid knew that irrational numbers existed. But to many people, a number that can't be written down was absurd. For centuries, many scientists and engineers believed that Φ was godlike.

This book discusses the myths from an engineering viewpoint. The last chapter of the book shows how Euclid handled irrational numbers; how Euclid did algebra using geometry; and a simple visual proof of why there are only five platonic solids.

This is a new release of the original 1952 edition.

An Unabridged Printing, To Include All Figures: The Basis Of Design In Nature - The Root Of Rectangles - The Leaf - Root Rectangles And Some Vase Forms - Plato's Most Beautiful Shape - A Brygos Kantharos And Other Pottery Examples Of Similar Rectangle Shapes - A Hydria, Stamnos, A Pyxis And Other Vase Forms - Further Analysis Of Vase Forms - Skyphoi - Kylikes - Vase Analysis Continues - Static Symmetry - Appendix

Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato hyperfunction theory.This book is concerned with, among others, local invariants that arise naturally in Complex Analytic Geometry and their relations with global invariants of the manifold or variety. The idea is to look at them as residues associated with the localization of some characteristic classes. Two approaches are taken for this -- topological and differential geometric -- and the combination of the two brings out further fruitful results. For this, on one hand, we present detailed description of the Alexander duality in combinatorial topology. On the other hand, we give a thorough presentation of the Čech-de Rham cohomology and integration theory on it. This viewpoint provides us with the way for clearer and more precise presentations of the central concepts as well as fundamental and important results that have been treated only globally so far. It also brings new perspectives into the subject and leads to further results and applications.The book starts off with basic material and continues by introducing characteristic classes via both the obstruction theory and the Chern-Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Various related topics are also discussed. The expositions are carried out in a self-containing manner and includes recent developments. The profound consequences of this subject will make the book useful for students and researchers in fields as diverse as Algebraic Geometry, Complex Analytic Geometry, Differential Geometry, Topology, Singularity Theory, Complex Dynamical Systems, Algebraic Analysis and Mathematical Physics.

The book Coordinate Geometry covers the concepts involved in the various topics of this subject. A few selected problems are solved after each chapter, to aid the understanding of the student. The book finishes with a collection of problems that the student must practice on, to gain expertise. The student is expected to make an honest attempt to solve the problems before looking at the suggested solutions. In doing so, the depth of understanding in the subject improves. Mathematics is not a spectator sport. It requires patience, perseverance and practice. The level of expertise in the subject in some sense is directly proportional to the number of problems solved by the student. The term solved is used to imply accuracy of thought, stringing together intermediate steps and accuracy of the final result. In a way, this term refers to the quality of the means to achieve the end goal for each problem. This book is intended to be a comprehensive self study guide for the students in middle & high schools.

A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties. Here, a class of such maps called semi-Riemannian maps is introduced. The main purpose of this book is to present results in semi-Riemannian geometry obtained by the existence of such a map between semi-Riemannian manifolds, as well as to encourage the reader to explore these maps.
The first three chapters are devoted to the development of fundamental concepts and formulas in semi-Riemannian geometry which are used throughout the work. In Chapters 4 and 5 semi-Riemannian maps and such maps with respect to a semi-Riemannian foliation are studied. Chapter 6 studies the maps from a semi-Riemannian manifold to 1-dimensional semi- Euclidean space. In Chapter 7 some splitting theorems are obtained by using the existence of a semi-Riemannian map.
Audience: This volume will be of interest to mathematicians and physicists whose work involves differential geometry, global analysis, or relativity and gravitation.

In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.