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Golden Ratio And Fibonacci Numbers, The
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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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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 one million books available in our catalogue for you to explore.
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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
- The Golden Ratio and Fibonacci Numbers
- CONTENTS
- PREFACE
- CHAPTER 1: INTRODUCTION
- CHAPTER 2: BASIC PROPERTIES OF THE GOLDEN RATIO
- CHAPTER 3: GEOMETRIC PROBLEMS IN TWO DIMENSIONS
- CHAPTER 4: GEOMETRIC PROBLEMS IN THREE DIMENSIONS
- CHAPTER 5: FIBONACCI NUMBERS
- CHAPTER 6: LUCAS NUMBERS AND GENERALIZED FIBONACCI NUMBERS
- CHAPTER 7: CONTINUED FRACTIONS AND RATIONAL APPROXIMANTS
- CHAPTER 8: GENERALIZED FIBONACCI REPRESENTATION THEOREMS
- CHAPTER 9: OPTIMAL SPACING AND SEARCH ALGORITHMS
- CHAPTER 10: COMMENSURATE AND INCOMMENSURATE PROJECTIONS
- CHAPTER 11: PENROSE TILINGS
- CHAPTER 12: QUASICRYSTALLOGRAPHY
- CHAPTER 13 : BIOLOGICAL APPLICATIONS
- APPENDIX I: CONSTRUCTION OF THE REGULAR PENTAGON
- APPENDIX II: THE FIRST 100 FIBONACCI AND LUCAS NUMBERS
- APPENDIX III: RELATIONSHIPS INVOLVING THE GOLDEN RATIO AND GENERALIZED FIBONACCI NUMBERS
- REFERENCES
- INDEX