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Fractal goldenratio1/3/2024 Golden ratio discovered in quantum world: Hidden symmetry observed for the first time in solid state matter / Helmholtz Association of German Research Centres, January 7, 2010 The skulls of less related species such as dogs, two kinds of monkeys, rabbits, lions and tigers, however, diverged from this ratio. In a new study investigating whether skull shape follows the Golden Ratio (1.618 … ), Johns Hopkins researchers compared 100 human skulls to 70 skulls from six other animals, and found that the human skull dimensions followed the Golden Ratio. Golden ratio observed in human skulls / Johns Hopkins University, October 3, 2019 Some recent discoveries relating to the Golden Ratio include: The ratio of a number to the previous number in the sequence approximates the Golden Ratio, and comes to approximate it more closely as the values increase. The Fibonacci sequence is derived by starting with 0 and 1, and then calculating the next number in the sequence by adding the last two together. The Golden Ratio also makes an appearance in the Fibonacci sequence. It is an irrational number that is a solution to the quadratic equation, with a value of: The Greek letter phi ( or ) represents the golden ratio. It is truly the mathematical language of the universe. In modern mathematics, the golden ratio occurs in the description of fractals, figures that exhibit self-similarity and play an important role in the study of chaos and dynamical systems. To get more technical, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.Ī golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. (In fact, the ratio is a number that begins 1.32472… and carries on forever).Can you impose its authority on earth? (Job 38:33) Also know the divine proportion, the golden section, and the golden number, the Golden Ratio describes a rectangle with a length roughly one and a half times its width. It turned out that the ratio 1.325, which gives you the rectangle that creates the Harriss spiral has been written about – it is known as the “ plastic number” – but Harriss could find no previous drawings of the spiral. His first concern was that maybe someone else had had, in fact, drawn the spiral “One thing about mathematical discoveries and mathematical art is that even if the process is completely new there is no guarantee that someone else has not already explored it.” “It’s more difficult to make something mathematically satisfying that people haven’t seen before.” “It’s not hard to make something that no one has seen before,” he said. But he was particularly delighted because he arrived at the spiral using a very simple mathematical process. Harriss was overjoyed when he first saw the spiral because it was aesthetically appealing – one of his primary aims was to draw branching spirals like you might find in Islamic art or the work of Gustav Klimt.
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