Braille y Matemática (written by) José Enrique Fernández del Campo
Table of Contents
Presentation ... 11
A) Century and a half after ... 11
— New symbolic-mathematical notations ... 11
— The language of graphic-geometric representations ... 12
— A powerful useful ... 13
B) Purpose of work ... 13
C) Instrumental budgets ... 14
D) Pre-requisite skills ... 17
1. Arithmetic ... 21
1.1. Writing Numbers ... 21
A) Integers and decimals ... 21
B) Fractions ... 23
C) Ordinals ... 25
D) Roman numbering ... 27
1.2. Arithmetic operations ... 27
1.2.1. Integer operations ... 31
1.2.2. Operations with whole fractions ... 36
1.2.3. Decimal operations ... 39
A) Addition and subtraction ... 39
B) Multiplication ... 40
C) Division ... 45
1.3. Iterated calculations ... 49
1.4. Units and measures ... 50
1.4.1. Measurements of geometric magnitudes ... 51
1.4.2. Physical-chemical measures ... 56
2. Algebra ... 61
2.1. Writing algebraic expressions ... 61
A) Distinction between letters and numeric expressions: the prefix of lowercase Latin ... 65
B) Brands and indices ... 65
C) Simple algebraic fractions ... 68
D) Roots ... 69
2.2. The 'linear character of Braille', or 'invisible parenthesis' ... 70
2.3. Of equations and inequations, or "prodigality in spaces" ... 77
2.4. Objective: simplicity ... 79
A) Simplification of subscripts ... 81
B) Locally superfluous notations ... 82
C) Substitution of notations ... 86
2.5. Specific algorithms ... 89
A) Division of polynomials ... 89
B) Multiplication of polynomials ... 95
2.6. Other notations ... 99
2.6.1. Functions ... 99
2.6.2. Logic and Theory of Sets ... 103
3. Geometric notations ... 109
3.1. Angles ... 110
3.2. Segments and arcs ... 113
3.3. Vectors, straight and semi-straight ... 115
3.4. Geometric figures ... 120
4. Tables and pictures ... 123
4.1. Accidental Modifications ... 123
4.1.1. Swap rows for columns ... 124
4.1.2. Preference for basic axles ... 126
4.1.3. Partitioning in access modules ... 129
4.2. Essential modifications to the structure ... 131
4.2.1. Tables of arithmetic operations ... 132
4.2.2. Use transformed data ... 138
4.3. Simplification conventions ... 140
4.3.1. Suppression of lines ... 140
4.3.2. Suppression of signs ... 144
4.3.3. Use of conventional signs ... 147
5. Draw in Braille. Other two-dimensional representations ... 151
5.1. Linear diagrams ... 153
5.2. Rectangular diagrams ... 160
5.2.1. Cartesian tables/diagram of correspondences and bi-relationships ... 160
5.2.2. Diagrams/maps of Karnaugh ... 165
5.3. Cartesian representations or by means of coordinates ... 171
5.3.1. Fundamental matrix of Cartesian coordinates ... 172
5.3.2. Stair functions ... 176
5.3.3. Histograms ... 180
5.4. Circular sector diagrams ... 186
5.5. General networks ... 191
5.5.1. Elementary networks ... 192
5.5.2. Branched shapes ... 200
A) Tree diagrams ... 200
B) Synoptic tables ... 207
5.6. Dynamic or concept structures. Flowcharts ... 217
Index ... 228