1st Edition - January 1, 1963

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  • Author: Edward Otto
  • eBook ISBN: 9781483222783

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Nomography deals with geometrical transformations, particularly projective transformations of a plane. The book reviews projective plane and collineation transformations in geometrical and algebraical terms. The geometrical approach aims at permitting the use of elementary geometrical methods in drawing collineation nomograms consisting of three rectilinear scales. The algebraical treatment concerns nomograms containing curvilinear scales. The text explains functional scales that include the graph of a function and a logarithmic scale. The book explores equations which can be represented by elementary methods without the use of a system of coordinates, some equations that require algebraic calculations, as well as nomograms with a binary field (lattice nomograms). The text investigates collineation monograms of many variables, elementary geometrical methods of joining nomograms, and also of nomograms consisting of two parts to be superimposed on each other. In addition to the Massau method and the criterion of Saint Robert, the book also applies the criteria of nomogrammability of a function to address mathematical problems related to the analysis of the methods in constructing nomograms. The book can be useful for mathematicians, geometricians, engineers, and researchers working in the physical sciences who use graphical calculations in their work.

Table of Contents

  • Foreword

    I. Introduction

    1 Nomograms

    2 Projective Plane

    3 Projective (Collineation) Transformations

    4 Analytical Representation of a Projective Transformation

    5 Rectilinear Coordinates. Correlation

    II. Equations with Two Variables

    6 Graph of a Function

    7 Functional Scale

    8 Logarithmic Scale

    9 Projective Scale

    III. Equations with Three Variables

    I. Collineation Nomograms

    10 Equations of the Form f1(u)+f2(v)+f3(w) = 0. Nomograms with Three Parallel Scales

    11 Equations of the Form 1/f1(u)+1/f2(v)+1/f3(w) = 0. Nomograms with Three Scales Passing Through a Point

    12 Equations of the Form f1(u)f2(v)=f3(w). Nomograms of the Letter N Type

    13 Equations of the Form f1(x)f2(y)f3(z)=1. Nomograms with Scales on the Sides of a Triangle

    14 Nomograms with Three Rectilinear Scales

    15 Nomograms with Curvilinear Scales

    16 The Cauchy Equation

    17 The Clark Equation

    18 The Soreau Equation of the First Kind

    19 The Soreau Equation of the Second Kind

    20 An Arbitrary Equation with Three Variables. Nomograms Consisting of Two Scales and a Family of Envelopes

    II. Lattice Nomograms

    21 General Form of Lattice Nomograms

    22 Rectilinear Lattice Nomograms

    IV. Equations with Many Variables

    23 Collineation Nomograms of Many Variables

    24 Elementary Geometrical Methods of Joining Nomograms

    25 Systems of Equations. Nomograms Consisting of Two Parts to be Superimposed on Each Other

    V. Problems of Theoretical Nomography

    26 The Massau Method of Transforming Nomograms

    27 Curvilinear Nomograms for the Equations f1(u)f2(v)f3(w) = 1, f1(u)+f2(v)+f3(w) = 0, f1(u)f2(v)f3(w) = f1(u)+f2(v)+f3(w)

    28 The Nomographic Order of an Equation. Kind of Nomogram. Critical Points

    29 Equations of the Third Nomographic Order

    30 Equations of the Fourth Nomographic Order

    31 Criteria of Nomogrammability of a Function

    32 Criterion of Saint Robert



Product details

  • No. of pages: 314
  • Language: English
  • Copyright: © Pergamon 1963
  • Published: January 1, 1963
  • Imprint: Pergamon
  • eBook ISBN: 9781483222783

About the Author

Edward Otto

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