| Preface | 5 |
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| Preface | 6 |
| Maths and nature photography | 8 |
| 1 Mathematical interplay | 17 |
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| Zebra stripes and number codes | 18 |
| How a number becomes a zebra | 20 |
| The chicken and the egg | 22 |
| The tortoise paradox | 24 |
| Discerning information from photos | 26 |
| Repeatability of experiments | 28 |
| Reproduction of water lilies | 30 |
| Transitivity and combinatorics | 32 |
| Cameras and hand luggage | 34 |
| Beyond the limits of microscopy | 36 |
| Endless loops | 38 |
| Mathematical crochet work | 40 |
| Ispiration through fascination | 42 |
| 2 The mathematical point of view | 45 |
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| Remarkably similar | 46 |
| Associations | 48 |
| Similar, but not by accident | 50 |
| Iterative shape approximation | 52 |
| Rhombic zones | 54 |
| Nets of skew rhombuses | 56 |
| Oblique parallel projections | 58 |
| Fibonacci and growth | 60 |
| Different scales | 62 |
| The volume of a wine barrel | 64 |
| Three simple rules | 66 |
| 3 Stereopsis or spatial vision | 69 |
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| Depth perception | 70 |
| Two projections in one image | 72 |
| Compound eyes | 74 |
| Distance tables | 76 |
| Lens eyes | 78 |
| Eyes with mirror optics | 80 |
| Using antennae for accuracy | 82 |
| Intersecting the viewing rays | 84 |
| Natural impressions | 86 |
| Photo stitching | 88 |
| Impossibles | 90 |
| Cuboid or truncated pyramid? | 92 |
| 4 Astronomical vision | 95 |
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| Sunset | 96 |
| Solar eclipse | 98 |
| When the sun is very low | 100 |
| Fata Morgana | 102 |
| The scarab and the sun | 104 |
| The law of Right Angles | 106 |
| The beginning of spring | 108 |
| The “wrong” tilt of the moon | 110 |
| The sun at the zenith | 112 |
| Central american pyramids | 114 |
| The arctic circle | 116 |
| The southern sky | 118 |
| 5 Helical and spiral motion | 121 |
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| Helicoid | 122 |
| Thrust or lift? | 124 |
| The spiral | 126 |
| Of king snails and king worms | 128 |
| Exponential growth | 130 |
| Helispirals | 132 |
| From formulas to animal horns | 134 |
| Millipedes and pipe surfaces | 136 |
| Scope of intelligence | 138 |
| 6 Special curves | 141 |
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| The catenary | 142 |
| Invariance under central projection | 144 |
| The parabola | 146 |
| Knots | 148 |
| Contours with cusps | 150 |
| Geodesic gifts | 152 |
| 7 Special surfaces | 155 |
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| The sphere | 156 |
| The sphere’s silhouette | 158 |
| Approximating curved surfaces | 160 |
| Flexible and versatile | 162 |
| Development | 164 |
| Puristic beauty | 166 |
| Stable and simple construction | 168 |
| Minimized surface tension | 170 |
| Minimal surfaces | 172 |
| Soap bubbles | 174 |
| 8 Reflection and refraction | 177 |
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| The spherical refl ection | 178 |
| Il Carnevale | 178 |
| 180 | 178 |
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| Mirror symmetry | 182 |
| The planar refl ection | 184 |
| Starfi sh and radial symmetry | 186 |
| The pentaprism | 188 |
| The billiard effect | 190 |
| Sound absorption | 192 |
| The optical prism | 194 |
| Rainbow theory | 196 |
| At the foot of the rainbow | 198 |
| Above the clouds | 200 |
| Spectral colours underwater | 202 |
| Colour pigments or iridescence? | 204 |
| Fish-eye perspective | 206 |
| Snell’s window | 208 |
| Total refl ection and image raising | 210 |
| A fi sh-eye roundtrip | 212 |
| 9 Distribution problems | 215 |
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| Even distribution on surfaces | 216 |
| Distribution of dew | 218 |
| Contact problems | 220 |
| A platonic solution | 222 |
| Spiky equal distribution | 224 |
| Elastic surfaces | 226 |
| Quite dangerous | 228 |
| Pressure distr
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