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SACRED GEOMETRY IN ALBUQUERQUE & SANTA FE, NEW MEXICO
Sacred Geometry is the blueprint of Creation and the genesis of all form. It is an ancient science that explores and explains the energy patterns that create and unify all things and reveals the precise way that the energy of Creation organizes itself. On every scale, every natural pattern of growth or movement conforms inevitably to one or more geometric shapes.
As you enter the world of Sacred Geometry you begin to see as never before the wonderfully patterned beauty of Creation. The molecules of our DNA, the cornea of our eye, snow flakes, pine cones, flower petals, diamond crystals, the branching of trees, a nautilus shell, the star we spin around, the galaxy we spiral within, the air we breathe, and all life forms as we know them emerge out of timeless geometric codes. Viewing and contemplating these codes allow us to gaze directly at the lines on the face of deep wisdom and offers up a glimpse into the inner workings of the Universal Mind and the Universe itself.
THE GREEKS KNEW
Pythagoras (560-480 BC), the Greek geometer, was especially interested in the Golden Section, and proved that it was the basis for the proportions of the human figure. He showed that the human body is built with each part in a definite Golden Proportion (Golden Mean) to all the other parts. Pythagoras' discoveries of the proportions of the human figure had a tremendous effect on Greek art. Every part of their major buildings, down to the smallest detail of decoration, was constructed upon this proportion.
The Parthenon was perhaps the best example of a mathematical approach to art using the Golden Mean.
The Platonic Solids
Platonic Solids are perfectly regular solids with the following conditions: all sides are equal and all angles are the same and all faces are identical. In each corner of such a solid the same number of surfaces collide. The Platonic solids feature prominently in the philosophy of Plato for whom they are named. They are the only five regular convex solids that can accurately be circumscribed by a sphere. Only five Platonic solids exist: tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron.
  
 
The solids and their regularities were discovered by the Pythagoreans and were called originally Pythagorean solids. The Greek philosopher Plato described the solids in detail later in his book "Timaeus" and assigned the items to the Platonic conception of the world, hence today they are well-known under the name "Platonic Solids."
The idea that all things are composed of four primal elements: earth, air, fire, and water, is attributed to Empedocles (circa 493-433 BCE), Greek philosopher, statesman, and poet. He was born in Agrigentum (now Agrigento), Sicily, and was a disciple of Pythagoras and Parmenides.
Remember the opposite forces, Yin and Yang, male and female, whose interaction created everything in the universe? Empedocles thought that active and opposing forces, love and hate, or affinity and antipathy, act upon these elements, combining and separating them into infinitely varied forms.
He believed also that no change involving the creation of new matter is possible; only changes in the combinations of the four existing elements may occur.
Empedocles died about 6 years before Plato was born.
LEONARDO DA VINCE KNEW
In the fifteenth century Leonardo da Vinci trained as a painter during the Renaissance and became a true master of the craft. His amazing powers of observation and skill as an illustrator enabled him to notice and recreate the effects he saw in nature, and added a special liveliness to his portraits. Curious as well as observant, he constantly tried to explain what he saw, and described many experiments to test his ideas. Because he wrote down and sketched so many of his observations in his notebooks, we know that he was among the very first to take a scientific approach towards understanding how the Golden Mean works and how we see it.
ZEISING & LE CORBUSIER KNEW
The Golden Mean reappears in the nineteenth century, through Zeising and Fechner, and then rises to a certain fashion in the third and fourth decade of the twentieth century, where Neufert and Le Corbusier get to know it. Le Corbusier (October 6, 1887 – August 27, 1965) wrote Le Modulor and Modulor 2 . In the time of the beginning of Historicism and of the great scientific discoveries and theories, Adolf Zeising (1810-76) began his researches on proportions in nature and art. In the book "Neue Lehre von den Proportionen des menschlichen Korpers" (1854) Zeising formulates the law of proportionality as the following:
"The division of the whole on the unequal parts looked proportional when the ratio of parts of the whole between themselves is the same that the ratio of them to the whole―the ratio, which gives the Golden Mean".
 NATURE KNOWS
Fibonacci sequences appear in biological settings, such as branching in trees, the spiral of shells, the curve of waves, the fruitlets of a pineapple, an uncurling fern and the arrangement of a pine cone. As the Fibonacci sequences progresses it approximates the Golden Mean.
Why does Phi appear in plants?
The answer seems to be, at least in some cases, evolution: survival of the fittest. The geometrical structures that contain the number Phi = 1.618034 are usually the best structures in terms of “use of available space”, therefore plants and animals have evolved to have that kind of structures in their bodies.
 The arrangements of leaves is the same as for seeds and petals. All are placed at 0.618034 leaves, (seeds, petals) per turn. In terms of degrees this is 0.618034 of 360° which is 222.492°. However, we tend to "see" the smaller angle which is (1 - 0.618034) x 360 = 0.381966 x 360 = 137.50776..°.
If there are Phi (1.618034) leaves per turn (or, equivalently, Phi = 0.618034 turns per leaf ),  then we have the best packing so that each leaf gets the maximum exposure to light, casting the least shadow on the others. This also gives the best possible area exposed to falling rain so the rain is directed back along the leaf and down the stem to the roots. For flowers or petals, it gives the best possible exposure to insects to attract them for pollination.
Why does Phi appear in humans?
Humans are also the consequence of the Golden Mean, from the Heavens to the DNA, from the Sonic Resonance of the Earth to the Alphabet of the Heart, from the Brain Wave Coherence, the Heart/Brain Sonic Resonance and the Encoded Heart Intelligence to the Wave Shape of Emotion.
Face and Teeth Golden Mean proportion
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DNA in the cell appears as a double-stranded helix referred to as B-DNA.
This form of DNA has a two groove in its spirals, with a ratio of Phi in the proportion of the Major groove to the Minor groove, or roughly 21 angstroms to 13 angstroms
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Mandelbrot Set (Video)
The discovery of Fractal Geometry
Named after Benoît Mandelbrot
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DANIEL WINTER KNOWS (Institute of HeartMath, Boulder Creek, California, August 1992)
HEART GEOMETRY
Current research at the Institute shows a possible link between coherent cardiac electricities and DNA programming. The output of the EKG machine is fed into a spectrum analyzer which shows the frequency content of the heart beat. When people who are skilled in mental and emotional self-management focus on loving or appreciating, the frequency content of their EKG (heart electricity) changes in a significant way. The distribution of the power content of the heart electricity is normally scattered and cancels out. This is called incoherent.
However, when love and other positive feelings are being experienced the distribution dramatically changes to a coherent and ordered pattern. This, by itself, is amazing, but even more amazing is the fact that the mathematical ratio between the power peaks is the same ratio as the Golden Mean ratio of Phi (1.618034). This ratio is the one that allows electrical power to change scales or harmonic octaves without losing any of its power or information carried in its modulation. The DNA of every cell in our bodies is built upon this same ratio.
There are many other examples of this ratio in cellular structures, but this discovery is especially important because it shows a direct link between the heart electricity and the DNA. In other words, the electricity of the heart programs the DNA much like a radio wave is sent through the air to your radio. The DNA is like a radio receiver and the heart is like the transmitter.
There is also new evidence appearing in the spectrum analysis showing that the heart electricities contain a highly ordered or encoded intelligence that is ultimately responsible for the instructions sent to the DNA. These waves from the heart are affected by people’s emotions and thoughts, so when people are processing negative emotions such as fear, anger or anxiety, the electricities are affected in a way that blocks the proper flow of information from reaching the DNA. If these types of negative patterns are experienced repeatedly over time it eventually manifests in disease. The symptoms of this are already well documented.
Doctors and researchers have known for many years that negative emotions and thoughts are the main cause of aging and many diseases. These negative patterns have also been linked directly to heart disease. New research also indicates that conscious generation of “heart frequencies” such as love, care, and appreciation has a positive, beneficial effect on immune system health and brain function, and can reverse the effect of negative stress patterns in the mental and emotional nature.
 Medical research has proven that the emotional state of mind programs the cell’s health more than perhaps any other factor (or it can be said that negative emotions distort the accurate flow of information). Dr. Manfred Clynes, author of Sentics, is well known for his work in mapping the wave shape of emotions and the invention of a pressure transducer and related equipment to measure the wave shape of emotion. His work has been tested in many different cultures around the world.
Notice that the Golden Mean ratio of Phi (1.618034) appears again in the emotion frequency of love.
Download the complete Research Report
FRACTAL GEOMETRY
The Mandelbrot set, named after Benoit Mandelbrot, is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers.
Its boundary exhibits complicated structure at all length scales from about 1 down as far as you wish (or as you computer will take you) to zero. In other words, it is a fractal. A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.
Nature is filled with fractals, but the manufactured world is mostly Euclidean. Technology developed without exploiting iteration across many scales. Yet the lessons of blind physical forces, and of billions of years of organic evolution, assert the importance of fractals. Recently, some industries have started exploiting fractal forms. Here are a few examples:
 Antenna design is a very tricky problem. Common designs are sensitive to only a narrow range of frequencies, and are not efficient if they are smaller than a quarter of the wavelength. This is a problem for small, portable antennas, such as those on cellular phones.
Fractal antenna designs can overcome some of these problems. Experiments have shown that antennas built with only a small number of iterations of a fractal process can exhibit sensitivity at several frequencies. As the number of iterations increases, the lowest frequency of the antenna gets lower, and additional higher frequencies are added. Also, fractal antennas can operate efficiently at 1/4 the size of more traditional designs.
Fractal patterns have been found in traffic flows, music, cardiology, electronics, meteorology, and more. All fractals are made by positive feedback, no matter what the medium. They are neither stable nor static. They teeter at the edge of chaos. A minute touch and they may fly into wild gyrations, but equally a massive heave may fail to budge them.
A truly remarkable thing about the Mandelbrot set is that it is not generated by long strings of incomprehensible equations, but rather by a simple recursive algorithm that can be embodied in a few lines of computer code. So the seemingly infinite complexity of the Mandelbrot set has a simple underlying order. Here one is reminded of Coleridge and his "unity in variety." Using this fractal as an archetype, one can say that two hallmarks of fractal systems are: (1) inherent hierarchical organization, and (2) self-similarity, i.e., the copies within copies within.
The more difficult question is whether nature's hierarchy manifests a physically meaningful degree of self-similarity. Certainly we would not expect to find the exact self-similarity seen in Fournier's fractal. But, for all their apparent differences, might not atomic, stellar and galactic systems be more self-similar than is currently thought? Einstein once commented: "It has often happened in physics that an essential advance was achieved by carrying out a consistent analogy between apparently unrelated phenomena."
 One of the properties of fractals is that they contain no information that gives you a sense of scale: little pieces of a fractal look like the whole thing, and in particular, if someone shows you a zoom in to a fractal, you can't tell if they've zoomed in by a factor of 10 or 10 million! Now, Nature's best fractals have this "detail in the detail" property for only a finite number of repetitions, and the cauliflower is one of the best examples. Its surface is made of big bumps. On the big bumps are smaller bumps, and on those, still smaller bumps, and so on. It's easy to visualize each big bump as a whole cauliflower in its own right. Indeed, although the right-hand picture is a zoom into the one on the left, it's not too hard to imagine that you are looking at a whole pile of cauliflower on display at your local supermarket.
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