Otto Nomography

1. Auflage 2014
ISBN: 978-1-4832-2278-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 42, 314 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

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.

Autoren/Hrsg.

Otto, Edward

Inhaltsverzeichnis

1;Front Cover;1
2;Nomography
;4
3;Copyright Page
;5
4;Table of Contents
;6
5;FOREWORD;8
6;CHAPTER I.
INTRODUCTION;10
6.1;1. Nomograms;10
6.2;2. Projective plane;12
6.3;3. Projective (collineation) transformations;17
6.4;4. Analytical representation of a projective transformation;35
6.5;5. Rectilinear coordinates. Correlation;53
7;CHAPTER II. EQUATIONS WITH TWO VARIABLES;61
7.1;6. Graph of a function;61
7.2;7. Functional scale;67
7.3;8. Logarithmic scale;74
7.4;9. Projective scale;78
8;CHAPTER III.
EQUATIONS WITH THREE VARIABLES;88
8.1;I. COLLINEATION NOMOGRAMS;88
8.2;10. Equations of the form f1(u)+f2(v)+f3(w) = 0. Nomograms with three parallel scales;88
8.3;11. Equations of the form 1/f1(u)+1/f2(v)+1/f3(w) = 0. Nomograms with three scales passing through a point;101
8.4;12. Equations of the form f1(u)f2(v) = f3(w). Nomograms of the letter N type;112
8.5;13. Equations of the form f1(x)f2(y)f3(z) = 1· Nomograms with scales on the sides of a triangle;119
8.6;14. Nomograms with three rectilinear scales;127
8.7;15. Nomograms with curvilinear scales;131
8.8;16. The Cauchy equation;141
8.9;17. The Clark equation;156
8.10;18. The Soreau equation of the first kind;162
8.11;19. The Soreau equation of the second kind;167
8.12;20. An arbitrary equation with three variables. Nomograms consisting of two scales and a family of envelopes;170
8.13;II. LATTICE NOMOGRAMS;176
8.14;21. General form of lattice nomograms;176
8.15;22. Rectilinear lattice nomograms;183
9;CHAPTER IV.
EQUATIONS WITH MANY VARIABLES;203
9.1;23. Collineation nomograms of many variables;203
9.2;24. Elementary geometrical methods of joining nomograms;218
9.3;25. Systems of equations. Nomograms consisting of two parts to be superimposed on each other;236
10;CHAPTER V.
PROBLEMS OF THEORETICAL NOMOGRAPHY;243
10.1;26. The Massau method of transforming nomograms;243
10.2;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);254
10.3;28. The nomographic order of an equation. Kind of nomogram.Critical points;266
10.4;29. Equations of the third nomographic order;273
10.5;30. Equations of the fourth nomographic order;285
10.6;31. Criteria of nomogrammability of a function;294
10.7;32. Criterion of Saint Robert;302
11;BIBLIOGRAPHY;311
12;INDEX;312