In this post, we will see the book *This Amazingly Symmetrical World* by *Lev Tarasov*.

As we had written in the earlier post with Tarasov’s Calculus, which was remade electronically using LaTeX typesetting engine, this is another of his books which have been recreated with LaTeX.

The amount of efforts put in creating this book has been amply rewarded as the result has been aesthetically very pleasing for me. And in the process, I have learned a lot more about LaTeX and its packages. Hope this small effort is found useful by all. In case you find any typos please comment on the post.

Some snapshots from the remade book:

Link to the git repo of the source files

README.md

The project has the LaTeX source files for the book This Amazingly Symmetrical

World by Lev Tarasov. We have used the scans of the book for images and have

not recreated any of the images.Though I would have liked to create all the pages, especially the cover and the

art till the title page using TiKZ, for now, I have created pdfs for those pages

in Inkscape. Purists may not like it, but at least in this version, that is how things are. Also the tables are not made using LaTeX, but are simple scans. Perhaps in a later version of the book, we will have these two issues sorted.The original typesetting of the book lets itself to be very well typeset with one of Edward Tufte’s book style implemented in LaTeX.

If there are any errors while typesetting, for example, references, or typos

please report them so that they can be addressed.As usual, you will need all the package files to compile the book correctly.

## Contents

Preface 13

**A Conversation 15**

## Part I Symmetry Around Us 23

**1 Mirror Symmetry 27**

1 An Object and Its Mirror Twin 27

2 Mirror Symmetry 30

3 Enantiomorphs 31

**2 Other Kinds of Symmetry 35**

4 Rotational Symmetry 35

5 Mirror-Rotational Symmetry

6 Translational Symmetry

7 Bad Neighbours 39

8 Glide Plane (Axis) of Symmetry

**3 Borders and Patterns 43**

9 Borders 43

10 Decorative Patterns 45

11 Pattern Construction 49

12 The ‘Lizards’ Design 51

**4 Regular Polyhedra 53**

13 The Five Platonic Solids 53

14 The Symmetry of the Regular Polyhedra 54

15 The Uses of the Platonic Solids to Explain Some Fundamental Problems 55

16 On the Role of Symmetry in the Cognition of Nature 57

**5 Symmetry In Nature 59**

17 From the Concept of Symmetry to the Real Picture of a Symmetrical World 59

18 Symmetry in Inanimate Nature. Crystals 61

19 Symmetry in the World of Plants 63

20 Symmetry in the World of Animals 66

21 Inhabitants of Other Worlds 69

**6 Order in the World of Atoms 71**

22 Molecules 71

23 The Puzzle of the Benzene Ring 72

24 The Crystal Lattice 73

25 The Face-Centred Cubic Lattice 74

26 Polymorphism 76

27 The Crystal Lattice and the External Appearance of a Crystal 77

28 The Experimental Study of Crystal Structures 78

29 The Mysteries of Water 79

30 Magnetic Structures 80

31 Order and Disorder 82

**7 Spirality In Nature 85**

32 The Symmetry and Asymmetry of the Helix 85

33 Helices in Nature 87

34 The DNA Molecule 89

35 The Rotation of the Plane of Light Polarization 91

36 Left and Right Molecules. Stereoisomerism 92

37 The Left-Right Asymmetry of Molecules and Life 93

## Part II Symmetry Around Us 97

**8 Symmetry and The Relativity of Motion 101**

38 The Relativity Principle 101

39 The Relativity of Simultaneous Events 102

40 The Lorentz Transformations 103

41 The Relativity of Time Periods 105

42 The Speed in Various Frames 106

**9 The Symmetry of Physical Laws 109**

43 Symmetry Under Spatial Translations 109

44 Rotational Symmetry 111

45 Symmetry in Time 112

46 The Symmetry Under Mirror Reflection 113

47 An Example of Asymmetry of Physical Laws 114

**10 Conservation Laws 117**

48 An Unusual Adventure of Baron Münchhausen 117

49 The Problem of Billiard Balls 118

50 On the Law of Conservation of Momentum 121

51 The Vector Product of Two Vectors 122

52 Kepler’s Second Law 123

53 Conservation of the Intrinsic Angular Momentum of a Rotating Body 126

**11 Symmetry and Conservation Laws 129**

54 The Relationship of Space and Time Symmetry to Conservation Laws 129

55 The Universal and Fundamental Nature of Conservation Laws 130

56 The Practical Value of Conservation Laws 133

57 The Example of the Compton Effect 134

58 Conservation Laws as Prohibiting Rules 136

**12 The World of Elementary Particles 139**

59 Some Features of Particles 139

60 The Zoo of Elementary Particles 141

61 Particles and Antiparticles 142

62 Particles, Antiparticles and Symmetry 146

63 Neutrino and Antineutrino 148

64 The Instability of Particles 149

65 Inter-conversions of Particles 152

**13 Conservation Laws and Particles 157**

66 Conservation of Energy and Momentum in Particle Reactions 157

67 The Conservation of Electric Charge and Stability of the Electron 159

68 The Three Conservation Laws and Neutrino 160

69 Experimental Determination of Electron Antineutrino 162

70 Electron and Muon Numbers. Electron and Muon Neutrinos 163

71 The Baryon Number and Stability of the Proton 165

72 Discrete Symmetries. CPT-Invariance 167

**14 The Ozma Problem 171**

73 What Is the Ozma Problem? 171

74 The Ozma Problem Before 1956 173

75 The Mirror Asymmetry of Beta-Decay Processes 174

76 The Mirror Asymmetry in Decay Processes and the Ozma Problem 175

77 The Fall of Charge-Conjugation Symmetry 176

78 Combined Parity 177

79 Combined Parity and the Ozma Problem 179

80 The Solution to the Ozma Problem 180

**15 Fermions and Bosons 183**

81 The Periodic Table and the Pauli Principle 183

82 Commutative Symmetry. Fermions and Bosons 184

83 Symmetrical and Antisymmetrical Wave Functions 185

84 The Superfluidity of Liquid Helium. Superconductivity 187

85 Induced Light Generation and Lasers 188

**16 The Symmetry of Various Interactions 189**

86 The Principal Types of Interactions 189

87 Isotopic Invariance of Strong Interactions. The Isotopic Spin (Isospin) 191

88 Strangeness Conservation in Strong and Electromagnetic Interactions 194

89 Interactions and Conservations 197

90 A Curious Formula 198

91 The Unitary Symmetry of Strong Interactions 199

**17 Quark-Lepton Symmetry 203**

92 Quarks 203

93 The Charmed World 207

94 Quark-Lepton Symmetry 208

95 A New Discovery 210

**A Conversation Between the Author and the Reader About the Role of Symmetry 213**

The Ubiquitous Symmetry 213

The Development of the Concept of Symmetry 215

Symmetry-Asymmetry 217

On the Role of Symmetry in the Scientific Quest for Knowledge 219

Symmetry in Creative Arts 222

**Literature 231**