Golden Ratio And Fibonacci Numbers, The
eBook - PDF

Golden Ratio And Fibonacci Numbers, The

  1. 170 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Golden Ratio And Fibonacci Numbers, The

About this book

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.

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Information

Publisher
World Scientific
Year
1997
Print ISBN
9789810232641
9789810232641
eBook ISBN
9789812386304
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics
3 
Fig. 
1.1. 
Some 
rectangles 
with 
different 
aspect 
ratios, 
a 
(shown 
by 
the 
numbers 
inside 
the 
rectangles). 
more 
definitive 
but 
certainly 
less 
direct. 
The 
$reat 
pyramid 
"he 
relationship 
of 
the 
golden 
ratio 
to 
the 
design 
of 
the 
great 
pyramid 
of 
Cheops 
has 
also 
been 
the 
subject 
of 
some 
speculation 
(see 
Verheyen 
1992). 
The 
great 
pyramid 
has 
a 
base 
edge 
length 
of 
about 
230 
m, 
a 
height 
of 
about 
147 
nt 
go 
thou^ 
about 
9.5 
m 
of 
this 
has 
weathered 
away) 
and 
an 
apex 
angle 
of 
a
p
p
~
~
~
t
e
l
y
a 
= 
63.43' 
(see 
Fig. 
1.2). 
This 
apex 
angle 
is 
very 
close 
to 
the 
apex 
angle 
of 
the 
golden 
rhombus 
(63.435') 
which 
has 
dimensions 
derived 
from 
the 
golden 
ratio 
and 
which 
is 
discussed 
in 
detail 
in 
Chapter 
12. 
It 
has 
been 
suggested 
that 
the 
designers 
of 
the 
great 
pyramid 
were 
conscious 
of 
the 
relationship 
of 
the 

Table of contents

  1. The Golden Ratio and Fibonacci Numbers
  2. CONTENTS
  3. PREFACE
  4. CHAPTER 1: INTRODUCTION
  5. CHAPTER 2: BASIC PROPERTIES OF THE GOLDEN RATIO
  6. CHAPTER 3: GEOMETRIC PROBLEMS IN TWO DIMENSIONS
  7. CHAPTER 4: GEOMETRIC PROBLEMS IN THREE DIMENSIONS
  8. CHAPTER 5: FIBONACCI NUMBERS
  9. CHAPTER 6: LUCAS NUMBERS AND GENERALIZED FIBONACCI NUMBERS
  10. CHAPTER 7: CONTINUED FRACTIONS AND RATIONAL APPROXIMANTS
  11. CHAPTER 8: GENERALIZED FIBONACCI REPRESENTATION THEOREMS
  12. CHAPTER 9: OPTIMAL SPACING AND SEARCH ALGORITHMS
  13. CHAPTER 10: COMMENSURATE AND INCOMMENSURATE PROJECTIONS
  14. CHAPTER 11: PENROSE TILINGS
  15. CHAPTER 12: QUASICRYSTALLOGRAPHY
  16. CHAPTER 13 : BIOLOGICAL APPLICATIONS
  17. APPENDIX I: CONSTRUCTION OF THE REGULAR PENTAGON
  18. APPENDIX II: THE FIRST 100 FIBONACCI AND LUCAS NUMBERS
  19. APPENDIX III: RELATIONSHIPS INVOLVING THE GOLDEN RATIO AND GENERALIZED FIBONACCI NUMBERS
  20. REFERENCES
  21. INDEX

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Yes, you can access Golden Ratio And Fibonacci Numbers, The by Richard A Dunlap in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over 1.5 million books available in our catalogue for you to explore.