Preface -- Preface -- Maths and nature photography -- 1 Mathematical interplay -- Zebra stripes and number codes -- How a number becomes a zebra -- The chicken and the egg -- The tortoise paradox -- Discerning information from photos -- Repeatability of experiments -- Reproduction of water lilies -- Transitivity and combinatorics -- Cameras and hand luggage -- Beyond the limits of microscopy -- Endless loops -- Mathematical crochet work -- Ispiration through fascination -- 2 The mathematical point of view -- Remarkably similar -- Associations -- Similar, but not by accident -- Iterative shape approximation -- Rhombic zones -- Nets of skew rhombuses -- Oblique parallel projections -- Fibonacci and growth -- Different scales -- The volume of a wine barrel -- Three simple rules -- 3 Stereopsis or spatial vision -- Depth perception -- Two projections in one image -- Compound eyes -- Distance tables -- Lens eyes -- Eyes with mirror optics -- Using antennae for accuracy -- Intersecting the viewing rays -- Natural impressions -- Photo stitching -- Impossibles -- Cuboid or truncated pyramid? -- 4 Astronomical vision -- Sunset -- Solar eclipse -- When the sun is very low -- Fata Morgana -- The scarab and the sun -- The law of Right Angles -- The beginning of spring -- The "wrong" tilt of the moon -- The sun at the zenith -- Central american pyramids -- The arctic circle -- The southern sky -- 5 Helical and spiral motion -- Helicoid -- Thrust or lift? -- The spiral -- Of king snails and king worms -- Exponential growth -- Helispirals -- From formulas to animal horns -- Millipedes and pipe surfaces -- Scope of intelligence -- 6 Special curves -- The catenary -- Invariance under central projection -- The parabola -- Knots -- Contours with cusps -- Geodesic gifts -- 7 Special surfaces -- The sphere -- The sphere's silhouette.

Approximating curved surfaces -- Flexible and versatile -- Development -- Puristic beauty -- Stable and simple construction -- Minimized surface tension -- Minimal surfaces -- Soap bubbles -- 8 Reflection and refraction -- The spherical refl ection -- Il Carnevale & geometry -- Mirror symmetry -- The planar refl ection -- Starfi sh and radial symmetry -- The pentaprism -- The billiard effect -- Sound absorption -- The optical prism -- Rainbow theory -- At the foot of the rainbow -- Above the clouds -- Spectral colours underwater -- Colour pigments or iridescence? -- Fish-eye perspective -- Snell's window -- Total refl ection and image raising -- A fi sh-eye roundtrip -- 9 Distribution problems -- Even distribution on surfaces -- Distribution of dew -- Contact problems -- A platonic solution -- Spiky equal distribution -- Elastic surfaces -- Quite dangerous -- Pressure distribution -- Fluctuations of weight -- Kissing numbers -- 10 Simple physical phenomena -- Newton's laws of motion -- Jet propulsion and suction -- Selective light absorption -- Relative velocities -- The aerodynamical paradox -- Flying in formation -- Form follows function -- Offspring on parachutes -- The fastest track -- Manoeuvering through curves -- Mathematics and bees -- Interferences -- Doppler effect and the Mach cone -- Sonic waves on strange paths -- Acceleration vs. constant speed -- Stroboscopic effect -- 11 Cell arrangements -- Reproduction of daisies -- Spirals or no spirals? -- Calculating rotation -- Voronoi diagrams -- Iterative Voronoi structures -- Columnar basalt -- 3D cells -- Random paths -- Winding curves -- Fractal sphere packing -- 12 The difference between big and small -- Decimal powers among animals -- 150 million years without change -- Legendary strength -- Where is gravity? -- Threads from protein -- Dangerous glue.

Giant elephant ears -- Floating coins -- Model and reality -- Scale-independent depth of fi eld -- Blurry decisions -- Fluids -- Fractions of a millisecond -- Flexible straws -- Biomass -- Like an oil bath -- Survival of the fi ttest -- 13 Tree structures and fractals -- Sum of cross-sections -- Systematic chaos -- Branching -- Wonderful coincidences -- Fractal contours -- Fractal pyramids -- Animals or plants? -- Mathematical ferns -- Fractal expansion -- Level curves -- From octahedrons to snowfl akes -- 14 Directed motion -- Non-round gears -- Transmission matters -- Robust and effi cient -- Light-footedness and reaction time -- Throwing parabola -- Jumping up high -- With a club and cavitation -- Toys of changing colour -- Flight acrobatics.