A new look at the world: fractal geometry
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
RBA
2012
|
| Series: | Everything is mathematical
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 142 S. Ill., graph. Darst. |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149694543167488 |
|---|---|
| adam_text | Contents
Preface
.............................................
Chapter
1.
The Evolution of Geometry:
Mandelbrot versus Euclid
...................................................................................................... 9
The terrible deity
.................................................................................................................................. 15
A snapshot of complexity, urban development and linguistics
.............................. 17
Cities, more than just maps
..................................................................................................... 20
Geometry and linguistics: is geometric thinking innate?
.................................... 22
The prominence of Euclid
............................................................................................................ 23
The birth of the infinite straight line
....................................................................................... 26
A step towards the infinite:
projective
geometry
...................................................... 28
Painting a canvas of a swimming pool
............................................................................ 29
Summing the angles of a triangle
............................................................................................... 32
A note on topology
..................................................................................................................... 35
Flying over Greenland: the model of the Universe
........................................................ 36
The
Erlangen
Programme: what is geometry?
.......................................................... 41
A grain of pollen and the geometry
ornature
................................................................... 43
Chapter
2.
The Unknown Dimension:
Mapping the Universe
............................................................................................................ 51
A Universe in a drop of water
...................................................................................................... 51
Infinity in a circle
.................................................................................................................................. 55
Wars and border lengths
................................................................................................................... 61
Everything depends on the scale used for measuring
................................................... 64
Coverings
................................................................................................................................................... 67
Curves that cover the plane
........................................................................................................... 71
The Peano curve
................................................................................................................................... 72
The Hubert curve
................................................................................................................................ 75
Triangles, sponges and snowflakes: the fractal dimension
........................................... 78
The dragon curve
................................................................................................................................. 88
Chapter
3.
Dalmatians and Dragons: Linear Fractals
............................................ 95
Puddings and tents
............................................................................................................................... 99
CONTENTS
The Devil s staircase
............................................................................................................................ 101
What do the following have in common: dust, snowflakes and sponges?
........ 103
A collage to reconstruct anything
.............................................................................................. 106
Chapter
4.
Order Disguised
...................................................................................................... 109
Did Mandelbrot discover the Mandelbrot set?
.................................................................. 109
Impulsive-compulsive calculations
............................................................................................ 112
Prisoner points or escaping from the labyrinth
................................................................. 113
The Universe in a grain of sand
.................................................................................................. 119
Variations on a theme
........................................................................................................................ 122
The sound of chaos
..................................................................................................................... 124
The search for a definition
............................................................................................................. 125
Nature is not fractal
............................................................................................................................. 127
Awakening from the deterministic dream
.................................................................... 128
A butterfly in Brazil and a moth in Singapore
.................................................................. 130
The attraction of chaos
..................................................................................................................... 133
Bibliography
............................................................................................................................................ 137
Index
............................................................................................................................................................. 139
A New Look
at the World
Fractal geometry
Many natural phenomena exhibit irregular and even chaotic
shapes that cannot be analysed using traditional geometry: the
sponginess of the clouds, the branches of trees, the zig-zags of
lightning bolts. We can seek insights into these apparently random
elements of nature in the revolutionary mathematical concept of
fractals, a new way of looking at the world based on the maxim,
the whole contains the part and the part the whole.
|
| any_adam_object | 1 |
| author | Binimelis Bassa, Maria Isabel |
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| discipline | Mathematik |
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| spelling | Binimelis Bassa, Maria Isabel Verfasser aut A new look at the world fractal geometry Maria Isabel Binimelis Bassa London RBA 2012 142 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Fraktalgeometrie (DE-588)4473576-5 gnd rswk-swf Fraktalgeometrie (DE-588)4473576-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431292&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431292&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Binimelis Bassa, Maria Isabel A new look at the world fractal geometry Fraktalgeometrie (DE-588)4473576-5 gnd |
| subject_GND | (DE-588)4473576-5 |
| title | A new look at the world fractal geometry |
| title_auth | A new look at the world fractal geometry |
| title_exact_search | A new look at the world fractal geometry |
| title_full | A new look at the world fractal geometry Maria Isabel Binimelis Bassa |
| title_fullStr | A new look at the world fractal geometry Maria Isabel Binimelis Bassa |
| title_full_unstemmed | A new look at the world fractal geometry Maria Isabel Binimelis Bassa |
| title_short | A new look at the world |
| title_sort | a new look at the world fractal geometry |
| title_sub | fractal geometry |
| topic | Fraktalgeometrie (DE-588)4473576-5 gnd |
| topic_facet | Fraktalgeometrie |
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