toresenior.blogg.se - The fibonacci sequence in nature

One thing to keep in mind, though, is that the Fibonacci numbers are not observed everywhere.

The ‘chambers’ of a Nautilus shell increase in size with a ratio of 1.61.

The number of spirals pointed left and right are consecutive numbers in the Fibonacci sequence. If you categorize these spirals into those pointed left and right, you will get two consecutive Fibonacci numbers. If you count the spirals present, once again, it is a number present in the Fibonacci sequence. Similarly, consider the arrangement of seeds in the center of a sunflower. An iris has three large petals on the outside and three inner petals. Most pineapples have either five, eight, thirteen or twenty-one spirals these are also Fibonacci numbers. The total number of petals of a flower is often a number present in the Fibonacci sequence, as with irises and lilies. Nautilus shells, one of the most iconic examples of the Fibonacci sequence, follow the proportional increase of 1.61. The Fibonacci sequence can be observed in a stunning variety of phenomena in nature. The ratio between two consecutive numbers converges to 1.61803… : ‘phi’, or as you might call it, the ‘golden ratio’. Something strange happens when the sequence approaches infinity. In this sequence, each number is the sum of the two numbers that precede it. In his famous work ‘ Liber Abaci’, he introduced a hypothetical problem involving rabbits and employed the sequence to find the number of rabbits after a certain period of time. The origin of this sequence is much contested, although it is commonly attributed to the Italian mathematician Leonardo Fibonacci. Often called ‘Nature’s Universal Rule’, the Fibonacci sequence is perhaps one of the most famous mathematical sequences. One such sequence in nature, that is both common and fascinating, is the Fibonacci sequence.

Finding such patterns and abstractions facilitates our understanding of the world around us.Īs it happens, several living organisms exhibit mathematical patterns too. On a more cosmic scale, the characteristic spiral of galaxies that we are all too familiar with is a result of the laws of gravitation and can be modeled as such. Similarly, meanders or bends in rivers find explanation in the branch of fluid dynamics pertaining to physics. So, it is just that identifying a crystal as a symmetrical, uniform structure helps us in making approximations about its aspects. Assuming the object as perfect helps our cause. Mathematics is an abstract language, and the laws of physics serve to apply these abstractions to the real world. Of course, perfect crystals do not really exist the physical world is rarely perfect. A ‘perfect’ crystal is one that is fully symmetrical, without any structural defects. The struggle to find patterns in nature is not just a pointless indulgence it helps us in constructing mathematical models and making predictions based on those models.Ĭonsider the example of a crystal. After all, mathematics is, in its very essence, a search for patterns of all kinds – and what better place to find such irregularities than nature itself? A closer look into nature leads to some very interesting implications about the underlying beauty of our universe. Philosophers and mathematicians have, for long, dedicated themselves to the cause of explaining nature, beginning from the very early ventures of ancient Greeks. “Mathematics is the science of patterns, and nature exploits just about every pattern there is.” – Ian Stewart, British mathematician