The golden ratio: the beautiful language of mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
RBA
2012
|
| Schriftenreihe: | Everything is mathematical
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 158 S. Ill., graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804149694118494208 |
|---|---|
| adam_text | Contents
Prefece
......................................................................................................................................................... 7
Chapter l.The Golden Ratio
.................................................................................................. 9
A golden world
...................................................................................................................................... 11
The secret of roses
........................................................................................................................ 13
Numbers
..................................................................................................................................................... 18
The definition of the golden ratio
............................................................................................. 21
Basic properties of the golden ratio
.......................................................................................... 25
The Fibonacci sequence
................................................................................................................... 31
Surprising numbers
............................................................................................................................. 36
The sum of Fibonacci sequence terms
........................................................................... 37
Pythagorean triples
...................................................................................................................... 38
The relationship between the numbers in the Fibonacci sequence
............ 41
The general term of the Fibonacci sequence
............................................................. 43
Pascal s triangle and Fibonacci s sequence
..................................................................... 44
Prime numbers in Fibonacci s sequence
........................................................................ 45
Chapter
2.
The Golden Rectangle
....................................................................................... 47
Division of a segment in mean and extreme ratio
.......................................................... 47
The shape of rectangles and the golden ratio
..................................................................... 49
Recognising and constructing a golden rectangle
.......................................................... 51
Construction of a golden rectangle
................................................................................... 55
Properties of the golden rectangle
..................................................................................... 56
Other notable rectangles
.................................................................................................................. 59
Rectangle
л/Г
...................................................................................................................... ............ 59
The silver rectangle
1 +
V2
................................................................................................. 61
The Cordovan rectangle
........................................................................................................... 61
Spirals and the golden ratio
............................................................................................................ 62
Chapter 3.The Golden Ratio and the Pentagon
..................................................... 67
The regular pentagon
......................................................................................................................... 67
The golden triangle
............................................................................................................................. 72
The symbolism of the star pentagon
........................................................................................ 74
Periodic and aperiodic tiles
............................................................................................................ 76
CONTENTS
The
Penrose
mosaics
........................................................................................................................... 83
Games
using the star pentagon and the golden ratio
.................................................... 86
Polyhedrons and the golden ratio
.............................................................................................. 88
Chapter
4.
Beauty and the Search for Perfection in Art
.................................... 95
About the Divine Proportions
............................................................................................................... 96
Leonardo: golden perfection
......................................................................................................... 99
The ideal measurements
........................................................................................................... 102
The golden ratio in painting
......................................................................................................... 103
The golden ratio and architecture
............................................................................................. 113
Contemporary architecture
.................................................................................................... 117
Le
Corbusier
.................................................................................................................................... 119
The golden ratio in design
............................................................................................................. 122
Chapter
5.
The Golden Ratio and Nature
..................................................................... 125
Growing shapes
..................................................................................................................................... 125
The golden ratio in living things
................................................................................................ 126
Phyllotaxis and the golden ratio
......................................................................................... 127
Flowers and petals
........................................................................................................................ 134
The nautilus
...................................................................................................................................... 135
Fractals and the golden ratio
........................................................................................................ 136
The snowflake fractal
.................................................................................................................. 137
End of the journey
............................................................................................................................... 142
Appendix: Original texts
.................................................................................................................. 143
Bibliography
............................................................................................................................................. 155
Index
............................................................................................................................................................. 157
The Golden Ratio
The beautiful language of mathematics
Can you express beauty in mathematical terms? Since
ancient times, the golden section (or golden ratio) has
been considered a yardstick for beauty, and mathematicians
have applied their theories to all manner of visual delights.
Discover, too, how the series of numbers identified by
Fibonacci obeys the rules of the golden ratio.
|
| any_adam_object | 1 |
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| bvnumber | BV040603289 |
| classification_rvk | SN 100 |
| ctrlnum | (OCoLC)823231174 (DE-599)BVBBV040603289 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T00:27:06Z |
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| spelling | Corbalán, Fernando Verfasser aut The golden ratio the beautiful language of mathematics Fernando Corbalán London RBA 2012 158 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Goldener Schnitt (DE-588)4021529-5 gnd rswk-swf Goldener Schnitt (DE-588)4021529-5 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=025431003&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=025431003&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Corbalán, Fernando The golden ratio the beautiful language of mathematics Goldener Schnitt (DE-588)4021529-5 gnd |
| subject_GND | (DE-588)4021529-5 |
| title | The golden ratio the beautiful language of mathematics |
| title_auth | The golden ratio the beautiful language of mathematics |
| title_exact_search | The golden ratio the beautiful language of mathematics |
| title_full | The golden ratio the beautiful language of mathematics Fernando Corbalán |
| title_fullStr | The golden ratio the beautiful language of mathematics Fernando Corbalán |
| title_full_unstemmed | The golden ratio the beautiful language of mathematics Fernando Corbalán |
| title_short | The golden ratio |
| title_sort | the golden ratio the beautiful language of mathematics |
| title_sub | the beautiful language of mathematics |
| topic | Goldener Schnitt (DE-588)4021529-5 gnd |
| topic_facet | Goldener Schnitt |
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