Download or read book Coordinate Geometry of Two Dimensions written by Hari Kishan and published by Atlantic Publishers & Dist. This book was released on 2006 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Present Book Coordinate Geometry Of Two Dimensions Aims At Providing The Students With A Detailed Study Of Polar Coordinates, Polar Equations Of A Straight Line And A Circle, Polar Equations Of Conics, General Equation Of Second Degree And System Of Conics The Topics Included In The Ugc Syllabus.Primarily Meant For Students Of B.Sc./B.A. Of Several Indian Universities, The Book Exactly Covers The Prescribed Syllabus. It Neither Includes The Irrelevant Nor Escapes The Essential Topics. Its Approach Is Explanatory, Lucid And Comprehensive. The Analytic Explanation Of The Subject Matter Is Very Systematic Which Would Enable The Students To Assess And Thereby Solve The Related Problems Easily. Sufficient Number Of High-Graded Solved Examples Provided In The Book Facilitate Better Understanding Of The Various Skills Necessary In Solving The Problems. In Addition, Practice Exercises Of Multiple Varieties Will Undoubtedly Prove Helpful In Quick Revision Of The Subject. The Figures And Also The Answers Provided In The Book Are Accurate And Verified Thoroughly.A Proper Study Of The Book Will Definitely Bring To Students A Brilliant Success. Even Teachers Will Find It Useful In Elucidating The Subject To The Students Of Mathematics.

Download or read book Two Dimensional Conformal Geometry and Vertex Operator Algebras written by Yi-Zhi Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Download or read book Two Dimensional Geometries A Problem Solving Approach written by C. Herbert Clemens and published by American Mathematical Soc.. This book was released on 2019-03-20 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space. One useful feature is that the book can be adapted to suit different audiences. The first half of the text covers plane geometry without and with Euclid's Fifth Postulate, followed by a brief synthetic treatment of spherical geometry through the excess angle formula. This part only requires a background in high school geometry and basic trigonometry and is suitable for a quarter course for future high school geometry teachers. A brief foray into the second half could complete a semester course. The second half of the text gives a uniform treatment of all the complete, simply connected, two-dimensional geometries of constant curvature, one geometry for each real number (its curvature), including their groups of isometries, geodesics, measures of lengths and areas, as well as formulas for areas of regions bounded by polygons in terms of the curvature of the geometry and the sum of the interior angles of the polygon. A basic knowledge of real linear algebra and calculus of several (real) variables is useful background for this portion of the text.

Download or read book Topology as Fluid Geometry written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second 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 second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. Volume 2 also includes a number of theorems usually assumed without proof since their proofs are not readily available, for example, the Zippin Characterization Theorem for 2-dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2-manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.

Download or read book Two dimensional Geometries written by Charles Herbert Clemens and published by . This book was released on 2019 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space. One useful feature is that the book can be adapted to suit different audiences. The first half of the text covers plane geometry without and with Euclid's Fifth Postulate, followed by a brief synthetic treatment of spherical geometry through the excess angle formula. This part only requires a background in high school geometry and basic trigonometry and is suitable for a quarter course for future high school geometry teachers. A brief foray into the second half could complete a semester course. The second half of the text gives a uniform treatment of all the complete, simply connected, two-dimensional geometries of constant curvature, one geometry for each real number (its curvature), including their groups of isometries, geodesics, measures of lengths and areas, as well as formulas for areas of regions bounded by polygons in terms of the curvature of the geometry and the sum of the interior angles of the polygon. A basic knowledge of real linear algebra and calculus of several (real) variables is useful background for this portion of the text

Download or read book Low Dimensional Geometry written by Francis Bonahon and published by American Mathematical Soc.. This book was released on 2009-07-14 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Download or read book Connected Mathematics written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a complete sixth grade mathematics curriculum with connections to other subject areas.

Download or read book Fundamentals of Hyperbolic Manifolds written by R. D. Canary and published by Cambridge University Press. This book was released on 2006-04-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Download or read book Shapes and Designs written by and published by . This book was released on 2009 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry Relativity and the Fourth Dimension written by Rudolf Rucker and published by Courier Corporation. This book was released on 2012-06-08 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

Download or read book Shapes and Designs written by Glenda Lappan and published by Pearson. This book was released on 1997 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Galactic Geometry written by Lisa Arias and published by Britannica Digital Learning. This book was released on 2019-06-01 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get ready to discover and uncover the properties of shapes. Learn all about dimensions, length, width, and 2- and 3-dimensional shapes. With the rhyming text in this book, you will discover hexagons, polygons, pentagons, and so much more in a fun and easy to understand way! So blast off and learn all about galactic geometry! This book will allow students to understand that attributes belonging to a category of 2- or 3-dimensional figures also belong to all subcategories of that category.

Download or read book A Texbook Of Two Dimensional Geometry written by and published by New Age International. This book was released on 1996 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: # Co-Ordinates# Equation Locus# Change Of Axes# Straight Line# Pair Of Straight Lines# Circle# Some Standard Curve# A Line And A Curve# Conic Sections# Parabola# Ellipse# Hyperbola# Tracing Of The General Conic# Polar Co-Ordinates.

Download or read book Three Dimensional Geometry and Topology Volume 1 written by William P. Thurston and published by Princeton University Press. This book was released on 2014-10-31 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Download or read book Two Dimensional Geometry written by Shalini Singh and published by . This book was released on 2000-01-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Shapes and Designs written by Glenda Lappan and published by . This book was released on 1995-01-01 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, students will explore shapes and their properties through creative investigations.

Download or read book The Greedy Triangle written by Marilyn Burns and published by Scholastic Inc.. This book was released on 1994 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introduction to polygons, a triangle convinces a shapeshifter to make him a quadrilateral and later a pentagon, but discovers that where angles and sides are concerned, more isn't always better.