Why is fibonacci famous

As a child, he travelled along with his father and amid his stay in Bugia he came across Hindu-Arabic numerals. He made acquaintance with a number of merchants during his trip through the Mediterranean coast, he learned their calculation methods. He was once a guest of an emperor who was inclined toward mathematics and science, Emperor Frederick II. Hence, he began writing a book on calculation system using that numeral system that resulted in the popularity of Hindu-Arabic numeral usage in the West.

The Republic of Pisa in granted Fibonacci a salary in a decree that was their way of honoring his services to the city as an advisor of accounting and other such important matters.

His magnum opus Liber Abaci brought the so-called modus Indorum to light. The digits 0—9 and place value were presented in the book and its practical use and value had been highlighted. Just in terms of pure mathematics - number theory, geometry and so on - the scope of his idea was so great that an entire professional journal has been devoted to it - the Fibonacci Quarterly.

Now let's look at another reasonably natural situation where the same sequence "mysteriously" pops up. Go back years to 17th century France. Blaise Pascal is a young Frenchman, scholar who is torn between his enjoyment of geometry and mathematics and his love for religion and theology. The Chevalier asks Pascal some questions about plays at dice and cards, and about the proper division of the stakes in an unfinished game.

Pascal's response is to invent an entirely new branch of mathematics, the theory of probability. This theory has grown over the years into a vital 20th century tool for science and social science. Pascal's work leans heavily on a collection of numbers now called Pascal's Triangle , and represented like this: This configuration has many interesting and important properties: Notice the left-right symmetry - it is its own mirror image.

Notice that in each row, the second number counts the row. There are endless variations on this theme. Next, notice what happens when we add up the numbers in each row - we get our doubling sequence. Now for visual convenience draw the triangle left-justified. Add up the numbers on the various diagonals Fibonacci could not have known about this connection between his rabbits and probability theory - the theory didn't exist until years later.

What is really interesting about the Fibonacci sequence is that its pattern of growth in some mysterious way matches the forces controlling growth in a large variety of natural dynamical systems. Quite analogous to the reproduction of rabbits, let us consider the family tree of a bee - so we look at ancestors rather than descendants.

In a simplified reproductive model, a male bee hatches from an unfertilized egg and so he has only one parent, whereas a female hatches from a fertilized egg, and has two parents. Here is the family tree of a typical male bee: Notice that this looks like the bunny chart, but moving backwards in time. The male ancestors in each generation form a Fibonacci sequence, as do the female ancestors, as does the total.

You can see from the tree that bee society is female dominated. The most famous and beautiful examples of the occurrence of the Fibonacci sequence in nature are found in a variety of trees and flowers, generally asociated with some kind of spiral structure. For instance, leaves on the stem of a flower or a branch of a tree often grow in a helical pattern, spiraling aroung the branch as new leaves form further out.

Picture this: You have a branch in your hand. Focus your attention on a given leaf and start counting around and outwards. Count the leaves, and also count the number of turns around the branch, until you return to a position matching the original leaf but further along the branch. This sequence, in which each number is the sum of the two preceding numbers, has proved extremely fruitful and appears in many different areas of mathematics and science. The Fibonacci Quarterly is a modern journal devoted to studying mathematics related to this sequence.

Many other problems are given in this third section, including these types, and many many more: A spider climbs so many feet up a wall each day and slips back a fixed number each night, how many days does it take him to climb the wall. A hound whose speed increases arithmetically chases a hare whose speed also increases arithmetically, how far do they travel before the hound catches the hare.

Calculate the amount of money two people have after a certain amount changes hands and the proportional increase and decrease are given. References show. Biography in Encyclopaedia Britannica. Storia Sci. J Weszely, Fibonacci, Leonardo Pisano c. Additional Resources show. Honours show. Merchants had to convert from one to another whenever they traded between these systems. Fibonacci wrote Liber Abaci for these merchants, filled with practical problems and worked examples demonstrating how simply commercial and mathematical calculations could be done with this new number system compared to the unwieldy Roman numerals.

The impact of Fibonacci's book as the beginning of the spread of decimal numbers was his greatest mathematical achievement. However, Fibonacci is better remembered for a certain sequence of numbers that appeared as an example in Liber Abaci. One of the mathematical problems Fibonacci investigated in Liber Abaci was about how fast rabbits could breed in ideal circumstances.

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits.

Suppose that our rabbits never die and that the female always produces one new pair one male, one female every month from the second month on. The puzzle that Fibonacci posed was How many pairs will there be in one year? At the end of the first month, they mate, but there is still only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits.

At the end of the third month, the original female produces a second pair, making 3 pairs in all. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produced her first pair also, making 5 pairs. Now imagine that there are pairs of rabbits after months. The number of pairs in month will be in this problem, rabbits never die plus the number of new pairs born.

But new pairs are only born to pairs at least 1 month old, so there will be new pairs. So we have which is simply the rule for generating the Fibonacci numbers: add the last two to get the next.

Following this through you'll find that after 12 months or 1 year , there will be pairs of rabbits. Bees are better The rabbit problem is obviously very contrived, but the Fibonacci sequence does occur in real populations. Honeybees provide an example. In a colony of honeybees there is one special female called the queen.

The other females are worker bees who, unlike the queen bee, produce no eggs. The male bees do no work and are called drone bees. Males are produced by the queen's unfertilised eggs, so male bees only have a mother but no father. All the females are produced when the queen has mated with a male and so have two parents.

Females usually end up as worker bees but some are fed with a special substance called royal jelly which makes them grow into queens ready to go off to start a new colony when the bees form a swarm and leave their home a hive in search of a place to build a new nest. So female bees have two parents, a male and a female whereas male bees have just one parent, a female. He has 1 parent, a female. He has 2 grandparents, since his mother had two parents, a male and a female.

He has 3 great-grandparents: his grandmother had two parents but his grandfather had only one. How many great-great-grandparents did he have?

Again we see the Fibonacci numbers :. Bee populations aren't the only place in nature where Fibonacci numbers occur, they also appear in the beautiful shapes of shells. To see this, let's build up a picture starting with two small squares of size 1 next to each other.

We can now draw a new square — touching both one of the unit squares and the latest square of side 2 — so having sides 3 units long; and then another touching both the 2-square and the 3-square which has sides of 5 units.

We can continue adding squares around the picture, each new square having a side which is as long as the sum of the latest two square's sides. This set of rectangles whose sides are two successive Fibonacci numbers in length and which are composed of squares with sides which are Fibonacci numbers, we will call the Fibonacci Rectangles. If we now draw a quarter of a circle in each square, we can build up a sort of spiral. The spiral is not a true mathematical spiral since it is made up of fragments which are parts of circles and does not go on getting smaller and smaller but it is a good approximation to a kind of spiral that does appear often in nature.

Such spirals called logarithmic spirals are seen in the shape of shells of snails and sea shells. The image below of a cross-section of a nautilus shell shows the spiral curve of the shell and the internal chambers that the animal using it adds on as it grows. The chambers provide buoyancy in the water. Fibonacci numbers also appear in plants and flowers. Some plants branch in such a way that they always have a Fibonacci number of growing points.

Flowers often have a Fibonacci number of petals, daisies can have 34, 55 or even as many as 89 petals! A particularly beautiful appearance of fibonacci numbers is in the spirals of seeds in a seed head. The next time you see a sunflower, look at the arrangements of the seeds at its centre. They appear to be spiralling outwards both to the left and the right. At the edge of this picture of a sunflower, if you count those curves of seeds spiralling to the left as you go outwards, there are 55 spirals.

At the same point there are 34 spirals of seeds spiralling to the right. A little further towards the centre and you can count 34 spirals to the left and 21 spirals to the right. The pair of numbers counting spirals curving left and curving right are almost always neighbours in the Fibonacci series. The same happens in many seed and flower heads in nature. The reason seems to be that this arrangement forms an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges.