# Understanding the Fibonacci Sequence and Golden Ratio – Fractal Enlightenment

The Fibonacci Sequence The Fibonacci sequence is possibly the most simple recurrence relation occurring in nature. It is 0,1,1,2,3,5,8,13,21,34,55,89, 144… each number equals the sum of the two numbers before it, and the difference of the two numbers succeeding it. It is an infinite sequence which goes on forever as it develops. The Golden Ratio/Divine Ratio or Golden Mean - The quotient of any Fibonacci number and it’s predecessor approaches Phi, represented as ϕ (1.618), the Golden ratio. This iteration can continue both ways, infinitely. The Golden Ratio can be seen from a Chambered Nautilus to a Spiraling Galaxy The Golden Ratio can be applied to any number of geometric forms including circles, triangles, pyramids, prisms, and polygons. Sunflowers have a Golden Spiral seed arrangement. If you graph any number system, eventually patterns appear. Our universe and the numbers not only go on infinitely linear, but even it’s short segments have infinite points. Image source Phi Golden Ratio

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J. C. Leyendecker Joseph Christian Leyendecker (March 23, 1874 – July 25, 1951) was one of the preeminent American illustrators of the early 20th century. He is best known for his poster, book and advertising illustrations, the trade character known as The Arrow Collar Man, and his numerous covers for The Saturday Evening Post.[1][2] Between 1896 and 1950, Leyendecker painted more than 400 magazine covers. During the Golden Age of American Illustration, for The Saturday Evening Post alone, J. C. Leyendecker produced 322 covers, as well as many advertisement illustrations for its interior pages.

13 unsolved mysteries that still need answers in 2015 From a missing plane to a vast city hidden beneath Earth, 2014 left many stones unturned. Although we made many discoveries over the course of 12 months, some of them led to even more puzzling questions. Will 2015 be the year our search for answers comes to an end? Here are the mysteries the world will try to unravel in the new year. What happened to the plane that vanished without a trace? Nature, The Golden Ratio and Fibonacci Numbers Plants can grow new cells in spirals, such as the pattern of seeds in this beautiful sunflower. The spiral happens naturally because each new cell is formed after a turn. "New cell, then turn, then another cell, then turn, ..." How Far to Turn?

Swami Vivekananda on the Secret of Work: Intelligent Consolation for the Pressures of Productivity from 1896 by Maria Popova “Every work that we do… every thought that we think, leaves such an impression on the mind-stuff…” In December of 1895, the renowned Indian Hindu monk and philosopher Swami Vivekananda, then in his early thirties, traveled to New York, rented a couple of rooms at 228 West 39th Street, where he spent a month holding a series of public lectures on the notion of karma — translated as work — and various other aspects of mental discipline. They attracted a number of famous followers, including groundbreaking inventor Nikola Tesla and pioneering psychologist and philosopher William James, and were eventually transcribed and published as Karma Yoga: The Yoga of Action (public library) in 1896. Among the most timeless of them is one titled “The Secret of Work,” in which Vivekananda examines with ever-timely poignancy the ways in which we mistake the doing for the being and worship the perspirations of our productivity over the aspirations of our soul. Donating = Loving

Awesome Character Drawings: AP Studio Art This article features an AP Studio Art Drawing project by Seokkyun Hong, completed while studying Art at Hillcrest High School, Dallas, Texas, United States, 2008. Seokkyun was awarded full marks for his Concentration component (6/6) and was featured on the official AP Collegeboard website, as a learning exemplar for others. His project is essential viewing for any high school Art student who wishes to draw imaginary, fantasy illustrations as part of a traditional Fine Art project. Every artwork in Seokkyun's AP Studio Art Concentration project demonstrates a superb understanding of composition and high level of technical skill. Colours have been selected carefully, uniting different parts of the work (for example, in the second work, the blue of the Pepsi can is repeated upon the character’s uniform, the coloured pencil in the foreground and the 'drawing' on the table).

Dark matter is the thread connecting galaxy clusters Simulations of the Universe on the largest scales show an unexpected resemblance to nerve cells in the human brain, with galaxy clusters playing the role of the cell body and thinner filaments of matter linking them like axons. Galaxy surveys (such as the Sloan Digital Sky Survey, or SDSS) show that galaxies do cluster like our simulations predict. But the filaments that should connect them have been harder to find. Most of the mass in the Universe is dark matter—material that neither emits nor absorbs light—and filaments are predicted to be mostly dark matter: no galaxies, little hot gas.

Golden Ratio The Idea Behind It Have a try yourself (use the slider): Beauty This rectangle has been made using the Golden Ratio, Looks like a typical frame for a painting, doesn't it? Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape. Do you think it is the "most pleasing rectangle"? Tree of the knowledge of good and evil In Genesis Motif Composition In the phrase, tree of knowledge of good and evil, the tree imparts knowledge of tov wa-ra, "good and bad".

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