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"The Cosmic Calculator Course" - Summary of Book
2
1) Nikhilam Multiplication 1
Other Bases 3
Numbers Above the Base 4
Proportionately 5
Squaring Numbers Near a Base 6
Multiplying Numbers Near Different Bases 7
A Summary 8
2) Doubling and Halving 9
Multiplying by 5, 50, 25 10
Dividing by 5, 50, 25 11
3) Fractions 13
Top-Heavy Fractions 13
Finding a Fraction of a Number 14
Equivalent Fractions 16
Simplifying Fractions 17
Finding what Fraction One Number is of Another 18
4) Spirals 20
The Isosceles Right-Angled Triangle 21
Spirals from Squares 22
An Infinite Sum 23
5) Decimals and Fractions 24
Converting Decimals to Fractions 24
Changing Fractions to Decimals 25
Comparing Fractions and Decimals 27
Recurring Decimals 27
Block Recurrers 28
Reciprocals 30
Prime Factors 31
REVISION Test 7
6) The Arithmetic of Bar Numbers 33
Addition and Subtraction 33
A Game 34 GAME
Applications in Algebra 36
Multiplication and Division 37
Brackets 38
Nikhilam Multiplication again 39
7) General Multiplication 41
Multiplying 3-Figure Numbers 45
Moving Multiplier 46
Written Calculations 47
8) Algebraic Multiplication 49
Multiplying and Dividing Single Terms 49
Multiplying Binomials 51
Factorising Quadratic Expressions 54
9) Squaring 55
The Duplex 55
Number Splitting 56
Algebraic Squaring 57
REVISION Test 8
THE MOEBIUS STRIP 59
10) Sequences 61
The nth Term 62
Sequences involving Fractions 65
11) Probability 66
Certain, Impossible and Uncertain 66
A Game 67 GAME
Scale of Probabilities 67
Possible Outcomes 68
Theoretical Probabilities 70
12) Equations 71
One Step Equations 71
Two-Step Equations 73
Three-step Equations 76
13) Angles and Triangles 78
Measuring Angles 78
Drawing Angles 81
Angles in a Triangle 82
Constructing Triangles 83
Isosceles Triangles 85
Calculating Angles 87
REVISION Test 9
14) Percentages 88
Converting a Percentage to a Fraction 88
Converting a Fraction to a Percentage 89
Important Percentages 90
Converting between Percentages, Fractions and Decimals 90
Finding a Percentage of a Quantity 91
Forming a Percentage 92
15) Forming Equations 94
16) 2 and 3 Dimensional Shapes 97
Dimensions 97
2-Dimensional Shapes 98
3-Dimensional Shapes 99
17) Straight Line Graphs 103
Sloping Lines 105
Gradient Squares 108
Gradients: By the Completion of the Triangle 109
Gradient and Intercept 109
Alternative Method using Substitution 111
18) Charts 113
Frequency Tables 113
Line Charts and Dot Diagrams 114
Bar Charts 115
Pictograms 116
Averages and Spread 117
REVISION Test 10
FRACTALS 119
19) Divisibility 121
Divisibility by 8 122
Higher Divisors 123
By Addition and By Subtraction 123
Cancelling Zeros 125
Divisibility by 11 127
20) Further Multiplication 128
Multiplying 3-figure Numbers 128
From Right to Left 130
4-Figure Numbers 131
Squaring 132
Special Numbers 133
Proportionately 134
Disguises 135
21) Combining Fractions 137
Addition and Subtraction 137
Comparing Fractions 140
A simplification 140
Multiplication and Division 141
A Simplifying Device 143
22) Arithmetical Operations 144
The Order of Operations 144
Two Puzzles 146
Brackets 146
Cancelling 148
Some Revision of Decimals 149
Multplication of Decimals 149
Decimal Division 151
23) Special Division 152
A Short Cut 153
Divisor Above a Base Number 156
REVISION Test 11
24) Percentage Changes 158
Increasing by 10% 159
Percentages Increases 160
Percentage Reductions 161
25) Transformations 163
Enlargement 163
Reflection 166
Rotation 168
Translation 171
26) Constructions 174
Bisecting a Line 174
Bisecting an Angle 176
Constructing Angles 177
The Golden Rectangle 178
The Pentagram 181
27) Bearings 183
Parallel Lines 183
Scale Drawing 186
Bearings 187
Using Bearings 188
REVISION Test 12
RANGOLI PATTERNS 192
HISTORICAL NOTES 194
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