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| CREATIVE
MATHEMATICS Part I |
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"The
real voyage of discovery
consists not in seeking new lands,
but seeing with new eyes"
Marcel
Proust
If
the word mathematics brings discomfort to your ears there
is hope on the horizon. Michael S. Schneider has written
a wonderful book that can dispel mathaphobia forever. After
reading A Beginner's Guide to Constructing the Universe,
your appreciation for the world of numbers will be elevated
and inspired. The title itself speaks volumes.
In
Schneider's own words, "A vision of mathematics different
from that which we were taught in school holds an accessible
key to a nearby world of wonder and beauty." The very essence
of form and life as we know it is built on numbers and their
inter-relationships. The creative archetype of nature is
number.
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Schneider does
an excellent job of bringing the art and science of numbers to a
level anyone can assimilate and grasp. The subtitle of the book
is The Mathematical Archetypes of Nature,
Art and Science. This book will permeate your psyche and spark
creative ideas. As you look around your world and everyday life
you will be illuminated by the simplicity and perfection of the
natural world and understand its mathematical relationships. Once
you grasp the essence of each number from one to ten the beauty
of mathematics will become clear.
The Beginner's
Guide takes you on a journey from the numbers one through ten.
In Part One of this review we will briefly delve into the numbers
one through five. In Part Two we will explore the numbers six through
ten. I will only give the barest hint here of what this book contains.
To get a full appreciation you need to purchase and savor the book.
It will be a book you treasure. Your children should read it, and
if they are too young to read, read it to them.
What Michael
does that sets this book apart from other writings on mathematics
is that he shows you how to create all geometric forms with the
three simple tools of a straight edge, a compass and a writing stylus.
All forms can be created with these three simple instruments. As
you take this journey you begin to get a feel for how nature has
constructed its myriad of structures from the simplest of tools.
This is only a brief example of what treasures of knowledge this
book holds. Let's begin. |
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ONE |
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"You
cannot conceive the many without the one..
The study of the unit is among those that lead the mind on
and turn it to the vision of reality."
Plato
The book begins
with a study of the initial Monad, the One, the source of all things.
Schneider points out, "The ancient philosophers conceived that the
Monad breathes in the void and creates all subsequent numbers (111111111
x 111111111 = 12345678987654321). Numbers only express different
qualities of the Monad." If you stop and contemplate the above equation
something very profound will reveal itself. The Monad expressed
nine times, multiplied by itself, produces all the subsequent numbers
progressively and then inversely.
Studying the
number One you also come to understand cycles. Circular rotary motion
is a principle of the Monad. All nature embodies these orbital circuits,
from the stars and galaxies to the atomic elements. Seasonal periodicities,
cyclic rhythms and spiraling vibrations permeate the universe and
touch our lives every day in every way. Learn why the simplest most
basic articles you use every day are based on circular principles
for their strength and resiliency. |
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TWO |
"Everything
that originated from the tree of knowledge carries in it duality."
Zohar
The circle
is the womb of creation. Yet the circle regenerated by creating
a mirror of itself. In this mirror is the first Dyad. It is said
that the void contemplated itself, reflected it's own light and
cast its own shadow. This was the beginning of all form and duality.
Contrast is absolutely necessary for the recognition of form. The
light defines the dark and vice versa. Magnetic fields are the purest
expression of the Dyad. Polar opposites attract and repel and the
world is woven between them.
The vesica
pisces or intersection of two circles is the opening of the womb
from which all five Platonic solids and volumes are created. Duality
creates polarities and we can feel this principle in everything
we engage. Many corporate logos utilize the vesica Pisces, TWA,
CBS, MasterCard and others. |
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THREE |
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But
every tension of opposites culminates in a release, out of
which comes the "third."
In the third, the tension is resolved and
the lost unity is restored."
Carl G. Jung
The triad
is most obvious to us as the beginning, middle and end; birth,
life and death; past present and future; thesis, antithesis
and synthesis. According to Greek philosopher Iamblichus,
"The triad has a special beauty and fairness beyond all numbers,
primarily because it is the very first to make actual the
potentialities of the Monad. Schneider reveals to us that
"A triangle is a statement about relationship and balance.
As the centers of the two circle repel and tug at each other,
a reconciling third point occurs naturally above the place
were the circles cross and agree.We see this balanced path
between extremes in periodic phenomena such as a swinging
pendulum and a heartbeat." |
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designing a universe you need triangles to create self-supporting
structures. Carpenters stabilize structures by bracing it with triangles.
Triangles provide strength, balance and efficiency of energy space
and materials. Many knots and braids utilize the principle of the
triad for strength and self-reinforcement. All color photography is
the blending of three basic colors, yellow, magenta and cyan. Nature
uses triads fluently. Notice how the triad is the basic design in
the butterfly above. |
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FOUR |
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"The
right thing is to proceed from second dimension to third, which
brings us,
I suppose, to cubes and other three dimensional figures."
Plato
The tetrahedron
is the simplest four sided solid composed of perfect triads. The
number four is the beginning of depth in space. The number four
is the mother of three-dimensional form. The number four permeates
our lives. We have the Four Corners of the globe; the four elements,
fire, air, water and earth; and four seasons.
A pyramid is
four triads poised upon a square. This is the strongest structure
known. The butterfly also utilizes four stages of life to complete
its life cycle. Beginning as a silent egg, is becomes a hungry green
caterpillar, rests in a cocooned pupa to emerge as a winged creature
at last. Human maturation is measured in childhood, adolescence,
adulthood, and old age. |
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FIVE |
"If
you would understand the invisible,
look carefully at the visible."
Talmud
Five
is the number of regeneration. Form is ripe and ready in three-dimensional
space, and now it is time for this form to recreate itself.
The Pentad is present everywhere. The human body expresses
the Pentad's symmetry in its five senses, five extensions
from the torso with each limb ending in five fingers or toes.
Pentagrams are stars we see fluently in advertising and corporate
logos. Most flags embody a five-pointed star somewhere in
their symbolism. Cut open an apple and you will notice that
the core is in the shape of a star. |
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The Pentad
is also the key to the self-generating number series knows as the
Fibonacci sequence. The Fibonacci series is created by zero and
one (nothing and everything) adding to itself successively. For
example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... The series is
a self-accumulating sequence that grows from within itself, it's
immediate past and takes nothing from outside the sequence for additional
growth. This is the essence to the Pentad's principle of regeneration,
self-replicating growth, which began from nothing and became everything.
Sacred geometry
is the study of how the universe was constructed through number
and form. After reading this book you will have an immense appreciation
and greater understanding of the world you live in. We will continue
this review in Part II and learn briefly about the numbers six through
ten. Michael Schneider also gives workshops with hands on approach
to creating all two and three-dimensional forms with the simple
tools of a compass and straight edge. The following link is a brief
synopsis of one of these Seminars.
To contact Michael for more information on when and where his next
workshop is you can email him at Michael
Schneider.
Everyone desiring
to increase their creative potential and creative mind should read
this book and absorb its message. Life is truly an elegantly ordered
creative system. Once this order is gleaned, even briefly, the interconnectedness
of all that exists is appreciated. The integrity of nature once
grasped has an elegance of its own. To see this unity and appreciate
it will enhance your own creative aspirations. |
| ©
J.L. Read, 1997. All Rights Reserved. |
| CREATIVE
MATHEMATICS Part II |
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| SUGGESTED
READING: |
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A
Beginner's Guide to Constructing the Universe
by
Michael S. Schneider
In the
spiral of the nautilus shell, in the veins of a maple leaf,
in the bonds of the benzene ring--everywhere he looks, Schneider
sees a cosmic geometry. Of course, the lines of this geometry
have long attracted the attention of probing minds, including
Pythagoras, Plato, the Psalmist, Demetrius, and Plotinus.
The author weaves the insights of these thinkers and many
more together in a tapestry of reflections (richly illustrated)
on celestial harmonies. Once initiated into the ancient
mysteries, the reader will recognize profound meanings--not
merely scientific utility--in squares, triangles, and other
common shapes. The reader needs no extraordinary expertise
in mathematics to explore these pages, just a relish for
intellectual adventure. Schneider helps us discover just
how much mental energy can fit within the circle of new
horizons.
$13.27

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| Entire
list of recommended titles |
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