81. Quantum Gravity Theory Everything Superstring Super String Fibonacci Series Numb quantum gravity fibonacci series sequence numbers Eric Bredesen caballa cabalakaballa quantum mechanics wave theory kabala kaballah priory sion preurie http://www.gravity.org/aa_quantum_gravity_theory.html

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82. Law Of Spiral Symmetry Transformation In the case of fibonacci s phyllotaxis the progress of symmetry order is presented The spiral numbers in the sunflower discs are in direct dependence on http://www.goldenmuseum.com/1607SpiralSymmetry_engl.html

Law of spiral symmetry transformation As is well known from biology a relative arrangement of very different sprouts arising in the cones of shoots is characterized by the "spiral symmetry". This arrangement principle was named "phyllotaxis" . On the surface of phyllotaxis forms, especially in the closely packed botanic structures (pine cone, pineapple, cactus, head of sunflower etc.), one can see clearly visible left- and right curved series of sprouts. As to the symmetry order of phyllotaxis forms there exists a practice to indicate it through the ratios of the numbers corresponding to the number of the left- and right-hand spirals. In accordance with the law of phyllotaxis such ratios are given by the number sequence generated by the Fibonacci recurrent relationship G n G n-1 G n-2 The most widespread types of phyllotaxis are those described through the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ... , the Lucas numbers 1, 3, 4, 7, 11, 18, ... or the number sequence 4, 5, 9, 14, 23, ... satisfying to the general recurrent formula (1). It is well known that the process of the collective fruit growing is accompanied at the certain stage by a modification of the spiral symmetry order. As this takes place the modification is strictly regular and corresponds to the general rule of constructing the recurrent number sequences generated by (1). In the case of Fibonacci's phyllotaxis the progress of symmetry order is presented through the sequence:

83. Geometry In The Natural World Along with the fibonacci Sequence (which is a wholenumber system Clear examplesof geometry (and Golden Mean geometry) in Nature and matter http://www.infinitetechnologies.co.za/articles/geometry1.html

GEOMETRY IN THE NATURAL WORLD The Golden Mean: The Golden Mean, or Golden Ratio as it is known, is an irrational number just like other important numbers such as Pi. This means that it cannot be completely represented by our currently used number system, except as a formula ( Sqr (5)-1)/2. Just like Pi (approx. 3.1416) - Phi, or the Golden Ratio, has an endless number of digits after its decimal point and with no repetition of the digits sequences. Therefore, like "Transcendental" numbers, its value can only be approximated (using our number system alone). What is the Golden Ratio, and why is it important? The Golden Ratio is approximately Besides for possessing some remarkable and unique characteristics, the Golden Mean is found in ALL living creatures on Earth. Along with the Fibonacci Sequence (which is a whole-number system approximating the Golden Ratio, discovered by Leonardo Pisano Fibonacci), this ratio is found in plants and animal life wherever one looks. For example, this ratio can be found in fingers one's hand, amongst many other places, and it is prevalent in the skeletal structure of all creatures. The Fibonacci Sequence is as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...

84. Sacred Geometry The value of pi is an irrational number, and pi to 39 decimal places is sufficient It can be derived from geometry or from a fibonacci sequence. http://www.inthelight.co.nz/spirit/sacredgeometry/sacredgeometry.htm

home Spirituality Sacred Geometry Page Details on this page is an extraction of some of the more interesting facts that have made an impression on me. See links for further research. PI The circumference of a circle is p (pi) times the diameter of the circle, where pi is approximately 3 1/7 (or 22/7 - these sacred numbers turn up frequently in Hindu texts and Rosicrucian literature), or 3.14, or about square root of 10. The value of pi is an irrational number, and pi to 39 decimal places is sufficient accuracy to calculate the circumference of the universe to within the radius of the hydrogen atom! Here it is to 100 decimal places (see here for 5000 decimal places): In Vedic Mathematics, Swami Sri Bharati Krsna Tirthaji Majaraja shows the vedic numeric code, and how a hymn in praise of the Lord Shri Krishna, the Lord Shri Shankara, is also the value of p /10 to 32 decimal places (and apparently a key to calculate it to any number of decimal place, which I do not know) - the Sanskrit is shown above, which you can decode in to syllables and the decoding key below. 1 ka, ta, pa, ya

85. Fibonacci Sequence Ratio The sequence 1,1,2,3,5,8,13,21, is called a fibonacci sequence named after Suppose another sequence is formed by starting with different numbers for http://www.geocities.com/CapeCanaveral/Lab/8972/lessons/fibonacci.html

Main Page Lessons Angles Pool ... Euclid Homework Geometry Hon Geometry Web Calc Pythagorean Square Root Fractions Trivia Impossibles Trivia Quiz Optical Quiz Other Links Math Links TI Calc Ham Radio Astronomy ... E-mail me! Ratios and the Fibonacci Sequence The sequence 1,1,2,3,5,8,13,21,... is called a Fibonacci sequence named after its discoverer, Leonardo Fibonacci. He lived in the 13th century, like a famous saint you may have heard of. The first two terms of the sequnce are 1 and 1. The idea is that the remaining terms are formed by adding the previous two terms. So the third term is 1+1=2, the next is 1+2=3, the next is 2+3=5, and so on.. The script in the web page computes the first few terms and calulates the ratio of the previous two terms. First Term (A) = Second Term (B) = Number of Terms to Compute (N) = Questions Do you think the ratio will always be the same? Press the "Compute" button and find out. Was your initial guess right? As the terms become larger, what happens to the values of the ratios? (you may have to increase the number of terms (N) ) Suppose another sequence is formed by starting with different numbers for the the first and second term, and continuing in the same way as the Fibonacci sequence (That is, adding the previous two terms to get the next term). Do you think you will get a different ratio?

86. Sacred Geometry - Fibonacci Revisited From A Human Perspective. Sacred geometry fibonacci revisited from a human perspective The fibonaccisequence is the mathematical expression of the fractal that apparently http://www.bethedream.net/fibpage.htm

The more we live, the more we love, the more we grow... "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed." Albert Einstein "As you think, you travel, and as you love, you attract. You are today where your thoughts have brought you; you will be tomorrow where your thoughts take you." James Lane Allen ** Free WebPage Translators in Multiple Languages** With your permission I would like to share a few things about the development of cosmic physics, spindoctors of the new millennium, and personal experience. I hope that the structure of my writing and the vocabulary is understandable. I Am quite open to questions should the need arise. I may not have all the answers. I have experienced many modes of communication over the years, yet I find that expressing myself authentically resonates with the integrity of my heart. Many messengers choose to use people who are open to channel and/or have a propensity for connecting with the etheric airwaves much like modern media outlets. They usually intend for you to believe them as undisputed truth. I ask that you not believe a thing I am about to present. Just read with an open mind and ask your own intelligence to reveal any truth.

87. The Sacred Geometry Of Sound And it is we ourselves who embody the geometry of the cosmos! As we know,the fibonacci sequence starts with the number 1, and proceeds by adding the http://www.spiritofmaat.com/archive/jan4/prns/williams.htm

88. EXPLORIT Science Center - Weekly Column Another word that has that ability is geometry. Can you identify the next 5numbers in the fibonacci sequence? Despite all the occurrences of fibonacci http://www.explorit.org/columns_00-02/apr21-00.html

Homepage 2000-2005 Column Index 1995-1999 Column Index Explorit Science Center Weekly Column This page contains the material submitted to the local paper - The Davis Enterprise - for Explorit Science Center's news column published in that paper on Fridays. April 21, 2000 By: Tom Wickersham GEOMETRY EXHIBIT IS A FEARLESS ATTRACTION Spider, test, audit. These are words that have the ability to strike fear into the hearts of many. Another word that has that ability is geometry. Things geometrical are the building blocks of the world around us, from the pyramids of the ancient Egyptians to the skyscrapers of today, from the wheels on your bicycle to the giant radar dishes pointed at the heavens above. Geometry is a tool humans have developed to look at and understand our world. It is useful in not only in creating these human-made objects, but it also helps us explore patterns and relationships in nature. In taking a close look at nature, we find that nearly all of the shapes we discover are variations of several basic shapes. The most elementary shapes such as the triangle, circle and spiral, can be found everywhere. Leaves can be simplified to triangular shapes, the eyes of most animals are spherical, and the spiral of a snail shell can be seen repeated in the pattern of a galaxy. It is not coincidence that these shapes are repeated; their repetition is evidence of the effectiveness of that geometry. The repetition of such designs also gives rise to patterns and symmetry. The beauty we detect in flowers, butterfly wings and even ourselves is founded in our appreciation of symmetry.

89. Untitled Document This experiment set the basis for what is called a fibonacci Sequence ; The ratio of any of the numbers to the one before it approaches a number which http://www.personal.psu.edu/users/m/d/mdg192/crystals.htm

90. Fibonacci Finder fibonacci Number Calculator. (Practice of geometry). A book on geometry basedon Euclid s Elements and On Divisions . • Flos, ~1225. (Flower). http://www.archimedes-lab.org/nombredormachine.html

Fibonacci's and related Number Calculators Find any Fibonacci's Number "How many pairs of rabbits can be bred from one pair in a year?" L. Fibonacci Fibonacci calculator Recursive numbers Applications Fibonacci's life ... Books and links The Fibonacci Series or the chrysodromos , lit. the "golden course") is a sequence of numbers first created by the Italian mathematician Leonardo di Pisa, or Pisano, known also under the name Fibonacci in 1202. It is a deceptively simple series, but its ramifications and applications are nearly limitless. Fibonacci's Calculator top In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = the n -th Fibonacci number F o F F F n F n-1 F n-2 F (-n) n-1 F n In words: you start with and , and then produce the next Fibonacci number ( F n ) by adding the two previous Fibonacci numbers: n = rank

91. Phi - Natures Special Number “geometry has two geat treasures one the Theorem of Pythagoras; In columnB we now have the ratio of each fibonacci number to the one before it. http://www.ed.mtu.edu/esmis/id169.htm

var TlxPgNm='id169'; Phi - Natures Special Number Educators' Science and Math Institute Series About the Series Goals Institutes ... ESMIS ISLAND HOPPING ACROSS THE CURRICULUM Phi ( f ) - Natures Special Number Jon Stasiuk Introduction: Mathematics is a wonderful subject for students interested in solving problems but seems to only be loved by a few. Students seldom get to appreciate the beauty and creativity that mathematics has to offer. This unit makes an attempt to show the student that mathematics isn't a subject to be studied by a few and actually exists in the real world. Students will explore the Fibonacci Sequence and the Golden Ratio using plants, pictures, algebra, geometry, and music. Rationale for the Project: “Geometry has two geat treasures: one the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel” - Johann Kepler ( 1571 - 1630) For years I have been using parts of this project at different times in my classes. I have never taught the golden ratio as a mini - stand alone - unit Overview of the Project: I have included many activities and non-traditional assignments that actively engage the students. I have found that this works well for the students that I am targeting for this lesson.

92. The Mathematical Formula For The Perfect Face Along with the fibonacci Sequence (which is a wholenumber system geometry isthe very basis of our reality, and hence we live in a coherent world http://www.cojoweb.com/phi.html

The mathematical formula for the perfect face! Sydney June 11, 2004 3:37:38 PM IST It is difficult to define perfect beauty as the parameters for a perfect face may vary according to individual preferences. However, scientists have narrowed down to a simple mathematical ratio of 1:1.618, otherwise known as phi , or divine proportion, to set standards of beauty. "Only one formula has been consistently and repeatedly present in all things beautiful, be it art, architecture or nature, but most importantly in facial beauty," The Sydney Morning Herald quoted US dentist Yosh Jefferson, who operates a website dedicated to divine proportion, as saying. "Ideal facial proportions are universal regardless of race, sex and age, and are based on divine proportions," he adds. He defines the formula and says, if the width of the face from cheek to cheek is 10 inches (25 centimetres), then the length of the face from the top of the head to the bottom of the chin should be 16.18 inches to be in ideal proportion. If you're keen to see how you measure up, keep in mind that the ratio of phi also applies to: + The width of the mouth to the width of the cheek.

93. A FIBONACCI PRIMER fibonacci connects with geometry even Pythagorean Triples and probability . Can you find a perfect number or two among the F s? http://www.iit.edu/~smile/ma8907.html

A FIBONACCI PRIMER Freeman, Larry Kenwood Academy 1956 West Hood Avenue 1-312-536-8850 Chicago IL 60660-2217 1-312-262-1840 Objectives 1) To share knowledge about an interesting but obscure facet of recreational mathematics which is accessable and interesting to junior and senior HS math students. 2) To challenge teachers and students alike to discover and perhaps prove many interesting properties of the Fibonacci sequence and its unexpected relationship with the geometry of the regular pentagon and with the theory of limits. Equipment and Materials Writing implements; hand calculator (scientific preferred); accurate millimeter scale. Teacher-prepared worksheets to calculate and display up to twenty elements of the classical Fibonacci Sequence ("CF") and several varieties of generalized Fibonacci- like sequences ("GS"). Teacher-prepared worksheets with several regular pentagons complete with all diagonals and with all vertices and intersections of diagonals labeled. Recommended Strategies Provide a brief explanation of who Leonardo of Pisa was, his dates and place in math history the rabbit problem is optional. Use proper terminology which means subscripting: We denote specific terms of GS with subscripts. The i-th term of CF is written as F

94. Pendants - Lotus Lazuli - Sacred Geometry Jewelry Art JEWELRY GALLERY lotus lazuli sacred geometry jewelry art by gretchen mcpherson The fibonacci sequence is a self-generating pattern of unfolding http://www.lotuslazuli.com/pendants4.htm

Necklaces Platonic Solids Earrings Pendants ... PURCHASE Pendants - Neck Rings Measurements are taken from center of the pendant, top to bottom and are given in millimeters, which is more descriptive than inches for these small sizes. CLICK HERE for meanings of the stones and birthstones (opens in a separate window) FLOWER OF LIFE pendant: The Flower of Life is an ancient symbol of the matrix of creation. Its interlocking circles allude to the mysteries of the fruit which contains its own seed - the holographic blueprint of self-generation encoded within. Clear quartz beads are woven together with wire and sterling silver beads to create this stunning pendant. 54 mm On a solid Sterling silver 16" neck ring choker P-22 P-22A or $70 with 128-facet quartz crystal beads FIBONACCI SEQUENCE neck ring: The fibonacci sequence is a self-generating pattern of unfolding beginning with 1, adding 1 to itself to get the next number, then adding the previous 2 numbers to get the next number in the sequence, (1+1=2, 1+2=3, 2+3=5, 3+5=8 and so on). In this necklace, the silver dangles increase according to the fibonacci sequence, 1:1:2:3:5:8:13:21 punctuated by 9 fine quality tigereye beads. On a solid Sterling silver 16" neck ring choker

95. Ceva's Theorem: A Matter Of Appreciation Dan Pedoe remarks in his geometry course The theorems of Ceva and Menelaus In general, if Fk denotes the kth fibonacci number, aFn×Fn square can be http://www.cut-the-knot.org/Generalization/CevaPlus.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Cut The Knot! An interactive column using Java applets by Alex Bogomolny A Matter of Appreciation October 1999 I have a recollection. Years ago, a childhood friend of mine, Boris, shared with me with excitement an unusual experience he had on a visit to the Tretj'yakov Art Gallery in Moscow. He was accompanied by a professional painter, a good acquaintance of his older sister. While Boris was making a round in one of the halls, he observed that the painter remained all that time on the same spot studying a certain picture. Curious, my friend asked the painter what was it about the picture that kept him interested in it for so long. According to Boris, the painter did not reply directly, but, instead, stepped over to the picture and covered a spot on the picture with a palm of his hand. "Have a look at the picture and think of what you see," he requested. After a while, he uncovered the spot, stepped back and asked Boris to have another look. Well, almost 4 decades later, with the names of the painter and the picture long forgotten, I still vividly remember Boris' excitement when he told me of how entirely different, deeper and more beautiful, the picture appeared to him then.

96. Science -- Sign In fibonacci number patterns and triangular patterns with intrinsic defects By controlling the geometry and the stress upon cooling, these patterns can be http://www.sciencemag.org/cgi/content/full/309/5736/909

You do not have access to this item: Full Text : Li et al., Triangular and Fibonacci Number Patterns Driven by Stress on Core/Shell Micr..., Science You are on the site via Free Public Access. What content can I view with Free Public Access If you have a personal user name and password, please login below. SCIENCE Online Sign In Options For Viewing This Content User Name Password this computer. Help with Sign In If you don't use cookies, sign in here Join AAAS and subscribe to Science for free full access. Sign Up More Info Register for Free Partial Access including abstracts, summaries and special registered free full text content. Register More Info Pay per Article 24 hours for US $10.00 from your current computer Regain Access to a recent Pay per Article purchase Need More Help? Can't get past this page? Forgotten your user name or password? AAAS Members activate your FREE Subscription

97. NLVM Number & Operations Manipulatives NLVM manipulatives for Number Operations. Turtle geometry icon Turtlegeometry – Explore numbers, shapes, and logic by programming a turtle to move. http://nlvm.usu.edu/en/nav/topic_t_1.html

Virtual manipulatives related to the NCTM standard. Bar Chart Base Blocks Base Blocks Addition Base Blocks Decimals ... Contact

98. The Fibonacci Numbers A directory of material related to the fibonacci numbers. http://math.holycross.edu/~davids/fibonacci/fibonacci.html

The Fibonacci Numbers This page is a directory of material related to the Fibonacci numbers. As it is a preliminary version and a work in progress, please be patient. If you have questions or comments, please send me e-mail: davids@math.holycross.edu A Course on the Fibonacci Numbers During the spring semester of the 1994-1995 academic year I taught a course called "The Fibonacci Numbers". Some materials from that course , including the syllabus and some lecture notes, are available over the Web. I will probably teach the course again in the spring semester of the 1996-1997 academic year. Mathematical material Bob Devaney (a Holy Cross grad) of Boston University has some marvellous material on the Fibonacci numbers' stunning appearance in the Mandelbrot set In case you want them, here are the first 500 Fibonacci numbers, in blocks of 100: 0 to 99 100 to 199 200 to 299 300 to 399 ... 400 to 499 I have compiled a lengthy list of factorizations of Fibonacci numbers, which I am converting to HTML as time allows. Some of the entries in the lists are hotlinks to factorizations. Many of these computations were performed with the assistance of the symbolic computation package Maple This section will be worked on during February 1996. Please check back.

99. Gulden2 It s closely connected with the fibonacci sequence and f has a value of 2) An other example of the use of the golden section in geometry can be found in http://mathsforeurope.digibel.be/Gulden.htm

I) What's the golden section ? The golden section is sometimes called the golden ratio or the golden mean or the divine proportion and is often denoted by the Greek letter phi j that is sometimes printed as f or by another Greek letter tau t It's closely connected with the Fibonacci sequence and f has a value of 1.618033988749894848204586834365638117720309179805... . We call it Phi. But where does this number come from? We start with a segment (length 1) and want to divide it into two parts x and 1-x such that x is mean proportional between 1-x and the total length. x 1-x We look for the positive solution x of the following equation and we call the relation 1:x the golden ratio. x² = 1 - x x² + x - 1 = D = 5 with x =( f ' and f f We notice that f ' and f have the same decimal part and that f f '+ 1 or f f f f But if f f + 1 then also f f f f . f f f f f f and f f f and f The geometric sequence 1, f f f f f f ,... has a special property: each element is the sum of its two predecessors. Therefore it is an additive sequence as the Fibonacci sequence. And for each additive sequence we have that the limit of u n+1 /u n (if n ) is again f II) The different applications.

100. Scott Hotton's Information Site Many of them have been based on the notion that the fibonacci numbers somehow Among the suggestions on how fibonacci numbers could promote survival are http://www.math.smith.edu/~zeno/

Meet Scott Hotton This is me with Barthelemule. Bart is not my cat though, he was just along for the ride. This is a histogram of a chaotic attractor with hidden symmetry I am a mathematical biologist at UC Merced. Currently I am researching neural net models of cognitive processes and I am collaborating with mathematicians at Smith college and a botanist at Harvard on modeling plant development. UC Merced is the first US research university of the 21st century. Its emphasis is on interdisciplinary research especially in biology. It is located just west of Yosemite national park. Recently I've taught mathematics courses while professor of Mathematics at Miami University . Miami University is not in Florida. The University of Miami is located in Miami Florida but Miami University is in Oxford Ohio . Miami University was founded 1809. This was just a few years after Ohio became a state and long before Florida was a part of the United States. In the almost 200 years since it was founded Miami University has grown into a well respected university both for its teaching and research.

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