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Fractal Recursions

Related:  Sequenze, frattali, geometrie sacre

The Philosopher Stoned: Rodin Fibonacci Wheel Symmetries I would like to take a slightly deeper look at the Fibonacci/Rodin number wheel. But first, a quick review of Marko Rodin's vortex based mathematics for those that aren't so familiar. It is based on reducing all numbers to whole numbers, for example 25 = 2+5 = 7 or 1.156 = 1+1+5+6 = 13 = 1+3 = 4. From this we see very interesting patterns emerge. It may seem simple at first, but I believe it has far-reaching applications some of which we have seen in the development of the Rodin Coil. Take a look at this simple multiplication table - thanks to Chris Te Nyenhuis for this. Notice first how 9 repeats itself always. These 6 remaining numbers can also be depicted as a doubling/halving circuit on the lazy infinity shape on this wheel. Now we turn to the Fibonacci wheel. Watch what happens when we run the Fibonacci series as Rodin numbers. First off, we notice that each number is directly opposite its inverted pair. 9 is 0, and 1 and 8 are the points of maximum potential.

Bisection of Yin and Yang The flag of South Korea (and of Kingdom of Korea from 1883) contains the ancient yin-yang symbol (Taijitu in Chinese, Tomoye in Japanese and Taegeuk in Korean) that represents the struggle, merger and co-existence of two opposites (could be hot/cold, male/female, sky/earth, moon/sun, etc.) In the diagram Yin (the negative aspect) is rendered in black, with Yang (the positive aspect) rendered in white. The symbol is composed of two regions of a circle separated by two semicircles of half the radius of the big circle. Solution 1 This one requires no proof. Solution 2 Part of the Yin (black) piece below the horizontal diameter of the big circle is a semicircle with area πR²/8, where R is assumed to be the radius of the big circle, so that the small semicircle is of radius R/2. Solution 3 The dashed circle has radius R/√2. Solution 4 The reflection in the horizontal diameter of the big circle creates a second Yin-Yang pair of regions whose borderline supplies the necessary cut. Solution 5 Reference

Nassim Haramein - Sacred Geometry and Unified Fields Physicist Nassim Haramein presents new concepts explaining how we are all interconnected and can access infinite knowledge. “My brain is only a receiver. In the Universe there is a core from which we obtain knowledge, strength, inspiration. I have not penetrated into the secrets of this core, but I know it exists.” As early as 9 years old, Nassim was already developing the basis for a unified hyper-dimensional theory of matter and energy, which he eventually called the “Holofractographic Universe.” Nassim Haramein was born in Geneva, Switzerland in 1962. Combining this knowledge with a keen observation of the behavior of nature, he discovered a specific geometric array that he found to be fundamental to creation, and the foundation for his Unified Field Theory emerged. This groundbreaking theory has now been delivered to the scientific community through peer-reviewed papers and presentations at international physics conferences. In addition to his scientific papers, Mr. Related Posts

Teachers' resource: Maths and Islamic art & design Tiles, fritware with lustre decoration, Kashan, Iran, 13th-14th century, Museum no. 1074-1875. © Victoria & Albert Museum, London This resource provides a variety of information and activities that teachers may like to use with their students to explore the Islamic Middle East collections at the V&A. It can be used to support learning in Maths and Art. Included in this resource are sections on: Principles of Islamic art and design Pre-visit activities Activities to do in the museum Activities to do back at school Islamic art explores the geometric systems that depend upon the regular division of the circle and the study of Islamic art increases appreciation and understanding of geometry. Approaching an abstract subject in a concrete way provides a means of extending maths into other curriculum areas. Islamic Middle East (Room 42) and South Asia (Room 41) are referred to in the Museum activities. National curriculum links Preparation for a visit Download octagon template (PDF file, 43.5 KB)

Sacred Geometry Introductory Tutorial by Bruce Rawles Great site on natural law and basics of sacred geometry….check it out!-A.M. In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. The Sphere (charcoal sketch of a sphere by Nancy Bolton-Rawles) Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. The Circle The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. The Point At the center of a circle or a sphere is always an infinitesimal point. Almost everywhere we look, the mineral intelligence embodied within crystalline structures follows a geometry unfaltering in its exactitude.

The Meaning of Sacred Geometry Most of us tend to think of geometry as a relatively dry, if not altogether boring, subject remembered from our Middle school years, consisting of endless axioms, definitions, postulates and proofs, hearkening back, in fact, to the methodology of Euclids Elements, in form and structure a masterly exposition of logical thinking and mental training but not the most thrilling read one might undertake in their leisure time. While the modern, academic approach to the study of geometry sees it as the very embodiment of rationalism and left brain, intellectual processes, which indeed it is, it has neglected the right brain, intuitive, artistic dimension of the subject. Sacred geometry seeks to unite and synthesize these two dynamic and complementary aspects of geometry into an integrated whole. Geometry as a Woman Further differentiating Sacred Geometry from the ordinary geometry of our school days is its’ relation to number and symbol. An old Masonic lecture from several centuries ago states:

About Sacred Geometry Introduction 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 ancients believed that the experience of Sacred Geometry was essential to the education of the soul. The gift of lightSource is that it actually allows you to experience that essential self within the designs of pure Source energy. As far back as Greek Mystery schools 2500 years ago, we as a species were taught that there are five perfect 3-dimensional forms -The tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. All types of crystals, natural and cultured. 1. 2. 3. 1. 2.

Metatron Origins[edit] The identification of Metatron with Enoch is not explicitly made in the Talmud although it does reference a Prince of the World who was young but now is old. However, some of the earliest kabbalists assumed the connection. There also seems to be two Metatrons, one spelled with six letters (מטטרון), and one spelled with seven (מיטטרון). Talmud[edit] The Talmud relates that Elisha ben Abuyah (a rabbi and Jewish religious authority born in Jerusalem sometime before 70 CE), also called Acher (אחר, "other", as he became an apostate), entered Paradise and saw Metatron sitting down (an action that is not done in the presence of God). The Talmud states, it was proved to Elisha that Metatron could not be a second deity by the fact that Metatron received 60 "strokes with fiery rods" to demonstrate that Metatron was not a god, but an angel, and could be punished.[5] The Babylonian Talmud mentions Metatron in two other places: Sanhedrin 38b and Avodah Zarah 3b. Etymology[edit]

The Math Behind the Beauty By M. Bourne Jessica Simpson What has mathematics got to do with beauty? Actually, a lot. Physical attraction depends on ratio. Our attraction to another person's body increases if that body is symmetrical and in proportion. Scientists believe that we perceive proportional bodies to be more healthy. Leonardo da Vinci's "Vitruvian Man", showing the golden ratio in body dimensions Leonardo da Vinci's drawings of the human body emphasised its proportion. (foot to navel) : (navel to head) Similarly, buildings are more attractive if the proportions used follow the Golden Ratio. Golden Ratio The Golden Ratio (or "Golden Section") is based on Fibonacci Numbers, where every number in the sequence (after the second) is the sum of the previous 2 numbers: We will see (below) how the Fibonnaci Numbers lead to the Golden Ratio: Physical Beauty Why do many people feel that Jessica Simpson is beautiful? This mask of the human face is based on the Golden Ratio. Her beauty is mathematical! Choose mask: Save typing!

Fibonacci Numbers and The Golden Section in Art, Architecture and Music This section introduces you to some of the occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. Contents of this page The icon means there is a Things to do investigation at the end of the section. 1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More.. The Golden section in architecture The Parthenon and Greek Architecture The ancient Greeks knew of a rectangle whose sides are in the golden proportion (1 : 1.618 which is the same as 0.618 : 1). The Acropolis (see a plan diagram or Roy George's plan of the Parthenon with active spots to click on to view photographs), in the centre of Athens, is an outcrop of rock that dominates the ancient city. Links Modern Architecture The Eden Project's new Education Building The Eden Project in St. California Polytechnic Engineering Plaza As a guiding element, we selected the Fibonacci series spiral, or golden mean, as the representation of engineering knowledge. The United Nations Building in New York Music Art