rdthakur 78gmail com Patterns in nature are visible
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Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and are modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, arrays, cracks and stripes. Early Greek philosophers studied these patterns, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. "The laws of nature are but the mathematical rdthakur 78@gmail. com
Fibonacci sequence Rabbits, rabbits. Leonardo Fibonacci was a well-travelled Italian who introduced the concept of zero and the Hindu-Arabic numeral system to Europe in 1200 AD. He also described the Fibonacci sequence of numbers using an idealised breeding population of rabbits. Each rabbit pair produces another pair every month, taking one month first to mature, and giving rdthakur 78@gmail. com
Nautilus Shell As if this were not enough, Leonardo of Pisa gave us another interesting, if less known gift of mathematics. If you have never heard of the Fibonacci sequence, don't worry. To be honest, the sequence sees little publicity these days outside of a Dan Brown novel and the occasionally nerdy conversation which may or may not involve warp core propulsion mechanics. However, the Fibonacci sequence is an amazing bit of numbers that ties nature and mathematics together in surprising ways. From deep sea rdthakur 78@gmail. com
Fibonacci spiral If you construct a series of squares with lengths equal to the Fibonacci numbers (1, 1, 2, 3, 5, etc) and trace a line through the diagonals of each square, it forms a Fibonacci spiral. Many examples of the Fibonacci spiral can be seen in nature, including in the chambers of ardthakur 78@gmail. com nautilus
Sunflower Evolutionarily speaking, the best way to ensure success is to have as many offspring as possible (ergo the Baldwin brothers). The sunflower naturally evolved a method to pack as many seeds on its flower as space could allow. Amazingly, the sunflower seeds grow adjacently at an angle of 137. 5 degrees from each other, which corresponds exactly to the golden ratio. Additionally, the number of lines in the spirals on a Sunflower is almost always a rdthakur 78@gmail. com number of the Fibonacci sequence.
Golden ratio (phi) The ratio of consecutive numbers in the Fibonacci sequence approaches a number known as the golden ratio, or phi (=1. 618033989. . . ). The aesthetically appealing ratio is found in much human architecture and plant life. A Golden Spiral formed in a manner similar to the Fibonacci spiral can be found by tracing the seeds of a sunflower from the centre rdthakur 78@gmail. com
Fibonacci spiral rdthakur 78@gmail. com
Fibonacci spiral Bighorn sheep Ovis canadensis rdthakur 78@gmail. com
Spirals: phyllotaxis of spiral aloe, Aloe polyphylla rdthakur 78@gmail. com
Spirals: phyllotaxis of spiral aloe, Aloe polyphylla rdthakur 78@gmail. com
Multiple Fibonacci spirals : seed head of Sunflower, Helianthus annuus. rdthakur 78@gmail. com
Multiple Fibonacci spirals : red cabbage in cross section rdthakur 78@gmail. com
Fibonacci patterns occur widely in plant structures including this cone of Queen sago, Cycas circinalis rdthakur 78@gmail. com
Fibonacci Spiral Aloe Leonardo of Pisa was born around 1170 AD in (of course) Pisa, Italy. While not quite as famous as some other Italian or Ninja Turtle Leonardos, we do have a lot to thank him for. His most notable contribution to your life is probably found on the top row of your keyboard. While traveling through North Africa, Leo discovered that the local number system of 0 -9 was far superior than the obscure combination of X's, V's and I's the Romans had invented a millennium earlier to confuse later generations of elementary school students. Leonardo brought this number system to Europe rdthakur 78@gmail. com
Pine Cone Like the sunflower, the pine cone evolved the best way to stuff as many seeds as possible around its core. Also, in what was surely an accident, it evolved into perhaps the best substitute for toilet paper when in a pinch. The golden ratio is the key yet again. As with the sunflower, the number of spirals almost always is a rdthakur 78@gmail. com
Human body The golden ratio is found throughout your body, all the way to your DNA. Here's one you can see for yourself, dear reader, if you're still with us. If you use your fingernail length as a unit of measure, the bone in the tip of your finger should be about 2 fingernails, followed by the mid portion at 3 fingernails, followed by the base at about 5 fingernails. The final bone goes all the way to about the rdthakur 78@gmail. com
fingernails. Again, it's Fibonacci at work and the ratio of each bone to the next comes very close to the golden ratio. Continuing with the length of your hand to your arm is, again, the golden ratio. Fibonacci applies even down to what makes you, you. A DNA strand is exactly 34 by 21 angstroms. The Fibonacci sequence is truly a wonder. The examples are vast, and go way beyond the scale of this article. The patterns in which a tree grows branches, the way water falls in spiderwebs, even the way your own capillaries are formed can all be linked to Fibonacci. Science is just beginning to understand the implications of this simple sequence andrdthakur 78@gmail. com some of the
Spiral Galaxies If we take the above spiral and rotate it around the central axis, we get an almost perfect approximation of a spiral galaxy. The Golden Ratio Most of the interesting things we find that relate to the Fibonacci sequence are actually more closely related to a number that is derived from Fibonacci, called the golden ratio. If we take each number of the Fibonacci sequence and divide it by the previous number in the sequence (i. e. 2/1, 3/2, 5/3, 8/5), a pattern quickly emerges. As the numbers increase, the quotient approaches the golden ratio, which is approximately 1. 6180339887. Approximately. The golden ratio actually predates Fibonacci and has been breaking the brains of western intellectuals for around 2400 years. Applications for the golden ratio have been found in architecture, economics, music, aesthetics, and, of course, nature. rdthakur 78@gmail. com
Geometric sequence rdthakur 78@gmail. com
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Zero - Placeholder and Number rdthakur 78@gmail. com
Infinity rdthakur 78@gmail. com
Fractals rdthakur 78@gmail. com
Fractal spirals: Romanesco broccoli showing self-similar form rdthakur 78@gmail. com
The growth patterns of certain trees resemble these Lindenmayer system fractals rdthakur 78@gmail. com
Pi rdthakur 78@gmail. com
Geometry - Human induced rdthakur 78@gmail. com
Parallel lines rdthakur 78@gmail. com
Shapes - Cones rdthakur 78@gmail. com
Shapes - Polyhedra rdthakur 78@gmail. com
Shapes - Perfect rdthakur 78@gmail. com
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Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Symmetry rdthakur 78@gmail. com
Cube rdthakur 78@gmail. com
Cube rdthakur 78@gmail. com
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Praise the Creator !! He is Great !!!
Thank You for Watching us !!
Compiled By Rupesh Dinkar Thakur, A. V. S. Vidyamandir, Virar, India rdthakur 78@gmail. com
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