Nomography, Volume 42

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

Bibliography

Index

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.