Easy to read and comprehend
Mathematicians with special interest in biology, physics, geography, astronomy, architecture, design, etc., and being prepared to take pictures at any time, might try to answer unusual questions like the followings: What do a zebra, a tiger shark, and a hard coral have in common? How is this with drying mud, wings of dragon flies, and the structures of leaves? What is the “snail king” and is there also a “worm king”? Which curves stay of the same type after being photographed? Do fishes see like we do if we look through a fisheye lens? Which geometric properties of an object have physical consequences? Which kinds of geometric patterns appear when waves are interfering? In this book you can find 180 double pages with at least as many questions of this kind. The principle to attack a problem is often similar: It starts with a photo that is for some reasons remarkable. In a short description an explanation is offered, including relevant Internet links. Additionally one can frequently find computer simulations in order to illustrate and confirm.
Spectacular photos and unusual views and insights which give rise to questions that are carefully explained with mathematics
You learn to see the world with different eyes.
Author(s): Georg Glaeser
Series: Edition Angewandte
Publisher: Ambra
Year: 2013
Language: English
Pages: 360
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
