Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will ...

Author: Victor Gutenmacher

Publisher: Springer Science & Business Media

ISBN: 0817641610

Category: Mathematics

Page: 156

View: 876

Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels

In this case we should question whether the underlying data line is truly linear, or whether it just appears linear for the data we have (a shallow curve ...

Author: Alan R. Jones

Publisher: Routledge

ISBN: 9781351661447

Category: Business & Economics

Page: 498

View: 541

Best Fit Lines and Curves, and Some Mathe-Magical Transformations (Volume III of the Working Guides to Estimating & Forecasting series) concentrates on techniques for finding the Best Fit Line or Curve to some historical data allowing us to interpolate or extrapolate the implied relationship that will underpin our prediction. A range of simple ‘Moving Measures’ are suggested to smooth the underlying trend and quantify the degree of noise or scatter around that trend. The advantages and disadvantages are discussed and a simple way to offset the latent disadvantage of most Moving Measure Techniques is provided. Simple Linear Regression Analysis, a more formal numerical technique that calculates the line of best fit subject to defined ‘goodness of fit’ criteria. Microsoft Excel is used to demonstrate how to decide whether the line of best fit is a good fit, or just a solution in search of some data. These principles are then extended to cover multiple cost drivers, and how we can use them to quantify 3-Point Estimates. With a deft sleight of hand, certain commonly occurring families of non-linear relationships can be transformed mathe-magically into linear formats, allowing us to exploit the powers of Regression Analysis to find the Best Fit Curves. The concludes with an exploration of the ups and downs of seasonal data (Time Series Analysis). Supported by a wealth of figures and tables, this is a valuable resource for estimators, engineers, accountants, project risk specialists as well as students of cost engineering.

Over a finite field, a curve can have only a finite number of points, ... line, which were given in Chapter 1, and bounds on the weight of an array on a ...

Author: Richard E. Blahut

Publisher: Cambridge University Press

ISBN: 9781139469463

Category: Technology & Engineering

Page:

View: 618

The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.

1 , ) the curve will not meet that perpendicular again ; since no point in the continuation of CF , on either side , can be equally distant from F and C. If ...

Author: United States. Bureau of Public RoadsPublish On: 1938

( 3 ) Right - of - way lines parallel to a center line that consists of tangents and curves with transitions cannot readily be described by metes and bounds ...

RIGHT - OF - WAY LINES IN RELATION TO TRANSITIONS There are three general ... way lines parallel to a center line that consists of tångents and curves with ...

On the curve C4 , the locus of the point P ( t ) = [ t4,13,12,1 , 1 ] ( or , if one prefers , on the line on which the parameter t varies ) one obtains a ...

Author: Mauro Beltrametti

Publisher: European Mathematical Society

ISBN: 3037190647

Category: Mathematics

Page: 491

View: 214

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.

Mean curvature constant , central equation for surface having , 77 ; related to peeudo - sphere , 77 , 120 ; asymptotic lines on , 78 ; possesses isometric ...

4.6.3 The Class of Curves Parametrizable by Lines A natural question is whether only the rational curves considered previously are those parametrizable by ...

Author: J. Rafael Sendra

Publisher: Springer Science & Business Media

ISBN: 9783540737254

Category: Mathematics

Page: 270

View: 494

The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Author: Luther Pfahler EisenhartPublish On: 2013-04-25

Scheffers (equations of a curve) Scherk, surface of Schwarz, formulas of Singular line of a surface Singular point of a surface Sinistrorsum Sphere, ...

Author: Luther Pfahler Eisenhart

Publisher: Courier Corporation

ISBN: 9780486159461

Category: Mathematics

Page: 496

View: 250

Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

The vectors B* axe the line coordinate vectors of the Bezier lines. Since B* and any multiple AB*, A ^ 0, represent the same line, the curve is not ...

Author: Pierre-Jean Laurent

Publisher: CRC Press

ISBN: 9781439863596

Category: Computers

Page: 490

View: 422

This volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Int

Another application is to determine the boundedness of the plane curve . 16.1 The projective line The projective curves we consider lie in the projective ...

Author: J.W. Rutter

Publisher: CRC Press

ISBN: 9781482285673

Category: Mathematics

Page: 384

View: 966

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.

Sketch the lines lightly with pencil and refer to the small design if you need to check how far out a line curves, or how far a point extends, ...

Author: Judy B. Dales

Publisher: C&T Publishing Inc

ISBN: 9781571200525

Category: Crafts & Hobbies

Page: 160

View: 315

Important Note about PRINT ON DEMAND Editions: You are purchasing a print on demand edition of this book. This book is printed individually on uncoated (non-glossy) paper with the best quality printers available. The printing quality of this copy will vary from the original offset printing edition and may look more saturated. The information presented in this version is the same as the latest edition. Any pattern pullouts have been separated and presented as single pages. If the pullout patterns are missing, please contact c&t publishing.