"The Cosmic Calculator Course" - Summary of Book 3

1) Recurring Decimals 1     
Recurring Decimal Patterns 3    WORKSHEET 4     
A Different Denominator 4     
A Short Cut 4     
Proportionately 6

2) Formulae 7     
Rearranging Formulae 10     
Applications 11     
(a+b)(a-b) 12

3) Squares, Cubes and Roots 14     
Square Roots of Perfect Squares 15     
Cubing (using Proportionately) 18     
Cube Roots of Perfect Cubes 22

4) Straight Division 23     
Short Division Digression 24     
Longer Numbers 26     
Decimalising the Remainder 27     
Negative Flag Number 28

5) Equations 31     
Some Variations 31     
Fractional Answers 32     
Two x Terms 33     
Forming Equations 35     
Quadratic Equations 37

REVISION Test 13

6) Polygons 38     
Angle Sum of Polygons 38     
Regular Polygons 41     
Other Polygon Angles 43     
Tessellations 44      WORKSHEET 5     
Semi-Regular Tessellations 45

7) Similar Triangles 48     
Congruent Figures 56

8) The Musical Scale 57     
The Notes of the Octave 58      WORKSHEET 6     
The True or Natural Scale 60     
Ratios of Notes 62     
Another Mode 63     
The Ghandava Veda Scale 64

9) Nets and Networks 65     
Cuboids and Prisms 66     
Pyramids 68     
Euler's Formula 69     
A Puzzle 71     
Networks 71

REVISION Test 14

THE VEDIC SQUARE       WORKSHEET 7 73

10) Probability 75     
Theoretical Probabilities 75     
Relative Frequency 76     
Mutually Exclusive Events 78     
Expected Number 79     
Combined Events 81

11) Pi 83     
To Estimate p 84     
Circumference of a Circle 85     
Area of a Circle 86

12) Volumes of Prisms & Pyramids 89     
Area of a Trapezium 89     
Volume of a Prism 91      WORKSHEET 8     
Volume of a Pyramid 93

13) Parabolic Curves 95     
A Third Method- By Alternate Elimination and Retention 97     
Parabolas 98

14) Sequences 101     
Square Numbers 102     
Cube Numbers 103     
Triangular Numbers 104     
A Power Sequence 104     
Games and Puzzles 105     
The Fibonacci Sequence 108     
A Summary 109

REVISION Test 15

15) Loci 110     
The Cycloid 112     
The Conic Sections 115      WORKSHEET 9

16) Motion 118     
Speed 118     
Travel Graphs 121     
Change of Speed 122     
Conversion Graphs 123

17) Auxiliary Fractions 126     
Auxiliary Fractions- First Type 126     
Denominators Ending in 8, 7, 6 127     
Auxiliary Fractions- Second Type 129     
Working 2, 3 etc Figures at a TIme 131

18) Surveys 133     
Frequency Polygons 133     
Pie Charts 134     
Grouping Data 136     
Designing a Questionnaire 137     
Scatter Diagrams 138     
Correlation 140

REVISION Test 16

CODES 141

19) Vectors 143     
Another Notation 145     
Adding Vectors 147

20) Simultaneous Equations 150     
Proportionately 153     
Solution by Substitution 155     
Two Special Types 156

21) Divisibility and Simple Osculators 157     
The Ekadhika 157     
Osculation 158     
Testing Longer Numbers 160     
Other Divisors 162     
The Negative Osculator 163

22) Square Roots 166     
Squaring 166     
First Steps 167     
Square Root of a Perfect Square 168     
General Square Roots 171

REVISION Test 17

23) Quadratic Equations 175     
Factorising Quadratic Expressions 176     
Solving Quadratic Equations by Factorisation 179     
Differential Calculus 180

24) Pythagoras'Theorem 184     
An Algebraic Formula 186     
Problems 189     
The Theorem in Reverse 191

25) Triples 192     
Equal Triples 193     
Types of Number 194     
Perfect Triples 194     
The Angle in a Triple 195     
Triples for 45°, 30° and 60° 196     
Generating Perfect Triples 197     
Finding the Code Numbers of a Triple 198

26) Proof 200     
Angle Sum of a Triangle 200     
Five Proofs using Areas 201     
Even and Odd Numbers 203     
Representing Numbers Algebaically 205     
Nikhilam Multiplication 206     
Perfect Triples 207     
Quadratic Equations 208

27) Coordinate Geometry 209     
Distance Between Two Points 209     
Gradient of a Line Joining Two Points 211     
Equation of a Line Through Two Given Points 212     
Intersection of Two Lines 213

REVISION Test 18

THE PLATONIC SOLIDS 215

HISTORICAL NOTES 217