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1st Edition, Volume 42 - January 1, 1963

Author: Edward Otto

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 2 2 7 8 - 3

Nomography deals with geometrical transformations, particularly projective transformations of a plane. The book reviews projective plane and collineation transformations in… Read more

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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.

ForewordI. Introduction 1 Nomograms 2 Projective Plane 3 Projective (Collineation) Transformations 4 Analytical Representation of a Projective Transformation 5 Rectilinear Coordinates. CorrelationII. Equations with Two Variables 6 Graph of a Function 7 Functional Scale 8 Logarithmic Scale 9 Projective ScaleIII. Equations with Three VariablesI. 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 EnvelopesII. Lattice Nomograms 21 General Form of Lattice Nomograms 22 Rectilinear Lattice NomogramsIV. 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 OtherV. 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 RobertBibliographyIndex

- No. of pages: 314
- Language: English
- Edition: 1
- Volume: 42
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483222783

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