Maths in nature fibonacci

Maths in Nature and fibonacci sereies are explained

1. Maths in Nature [email protected] FIBONACCI SEQUENCE 1,1,2,3,5,8,13,21,. . .

2. Maths in Nature 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 thoughts of God"                         - Euclid [email protected]

3. Rabbits, rabbits, rabbits. Leonardo Fibonacci was a well-travelled Italian who introduced the concept of zero and the Hindu-Arabic numeral system to Europe in 1200AD. 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 the sequence 0,1,1,2,3,5,8,13,... Each number in the sequence is the sum of the previous two. Fibonacci sequence [email protected]

4. 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 creatures to flowers to the make-up of your own body, Fibonacci is everywhere. Nautilus Shell [email protected]

5. 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 a nautilus shell. Fibonacci spiral [email protected]

6. 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 number of the Fibonacci sequence. [email protected]

7. 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 outwards. [email protected]

8. Fibonacci spiral [email protected]

9. Fibonacci spiral Bighorn sheep Ovis canadensis [email protected]

10. Spirals: phyllotaxis of spiral aloe , Aloe polyphylla [email protected]

11. Spirals: phyllotaxis of spiral aloe , Aloe polyphylla [email protected]

12. Multiple Fibonacci spirals : seed head of Sunflower , Helianthus annuus . [email protected]

13. Multiple Fibonacci spirals : red cabbage in cross section [email protected]

14. Fibonacci patterns occur widely in plant structures including this cone of Queen sago, Cycas circinalis [email protected]

15. 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 and eventually we invented Sudoku with it. [email protected]

16. 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 Fibonacci number. [email protected]

17. 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 [email protected]

18. middle of your palm, which is a length of about 8 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 c apillaries are formed can all be linked to Fibonacci. Science is just beginning to understand the implications of this simple sequence and some of the most amazing discoveries may be yet to come. [email protected]

19. Spiral Galaxies If we take the above spiral and rotate it around the 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. [email protected]

20. Praise the Creator !! He is Great !!! [email protected]

21. Thank You for Watching us !! [email protected]

22. Compiled By Rupesh Dinkar Thakur, A. V. S. Vidyamandir , Virar , India [email protected] [email protected]