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What is the importance of the fibonacci sequence
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The Fibonacci numbers were first discovered by a man named Leonardo Pisano. He was known by his nickname, Fibonacci. The Fibonacci sequence is a sequence in which each term is the sum of the 2 numbers preceding it. The first 10 Fibonacci numbers are: (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89). These numbers are obviously recursive.
Fibonacci was born around 1170 in Italy, and he died around 1240 in Italy. He played an important role in reviving ancient mathematics and made significant contributions of his own. Even though he was born in Italy he was educated in North Africa where his father held a diplomatic post. He did a lot of traveling with his father. He published a book called Liber abaci, in 1202, after his return to Italy. This book was the first time the Fibonacci numbers had been discussed. It was based on bits of Arithmetic and Algebra that Fibonacci had accumulated during his travels with his father. Liber abaci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. This book, though, was somewhat contraversial because it contradicted and even proved some of the foremost Roman and Grecian Mathematicians of the time to be false. He published many famous mathematical books. Some of them were Practica geometriae in 1220 and Liber quadratorum in 1225.
The Fibonacci sequence is also used in the Pascal trianle. The sum of each diagnal row is a fibonacci number. They are also in the right sequence: 1,1,2,5,8.........
Fibonacci sequence has been a big factor in many patterns of things in nature. One has found that the fractions u/v representing the screw-like arrangement of leaves quite often are members of the fibonacci sequence. On many plants, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. Fibonacci nmbers are also used with animals. The first problem Fibonacci had wehn using the Fibonacci numbers was trying to figure out was how fast rabbits could breed in ideal circumstances. Using the sequence he was ale to approximate the answer.
The Fibonacci numbers can also be found in many other patterns. The diagram below is what is known as the Fibonacci spiral.
As I showed those examples, There are so many patterns of chord progressions but I want to focus on 2-5-1 chord progression.
Yang Hui has been found to be the oldest user of Pascal’s Triangle. But it is Blaise Pascal who around the year 1654 was credited for his extensive work on the many patterns of this triangle. Because of this people began to call it Pascal’s Triangle.
It is amazing to see how mathematics has such an influence on the world and the evidence it creates. The world is affected by numbers and mathematics all the time and this mysterious number known as the golden number has proven to be the center of everything.
Therefore the sequence 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, is called a recursive sequence. When the recursive numbers are arranged in a certain way, this sequence creates a spiral pattern and this pattern is reflected in various places in real life (nature).
Fibonacci was born in approximately 1175 AD with the birth name of Leonardo in Pisa, Italy. During his life he went by many names, but Leonardo was the one constant. Very little is known of his early life, and what is known is only found through his works. Leonardo’s history begins with his father’s reassignment to North Africa, and that is where Fibonacci’s mathematical journey begins. His father, Guilielmo, was an Italian man who worked as a secretary for the Republic of Pisa. When reassigned to Algeria in about 1192, he took his son Leonardo with him. This is where Leonardo first learned of arithmetic, and was interested in the “Hindu-Arabic” numerical style (St. Andrews, Biography). In 1200 Leonardo ended his travels around the Mediterranean and returned to Pisa. Two years later he published his first book. Liber Abaci, meaning “The Book of Calculations”.
Pierre de Fermat was born in the town of Beaumont-de-Lomagne in southwestern France at the beginning of the seventeenth century in the year 1601. Being the son of a wealthy merchant, Fermat was able to gain a privileged education at monasteries and universities. The young man, however, never showed any particular strength in the subject of mathematics, choosing instead to pursue a career in the civil service of France. His elevated status in society allowed him to include the “de” in his surname. He suffered a serious attack of the plague during his adult life, severe enough to prompt friends to mistakenly pronounce him dead! Fermat never made math his career, but mathematics at th...
Many types of problems are naturally described by recurrence relations said difference equations [2, 3], which usually
By 1904 Ramanujan had begun to undertake deep research. He investigated the series (1/n) and calculated Euler's constant to 15 decimal places. He began to study the numbers, which is entirely his own independent discovery.
Fermat was born in 1601 in Beaumont-de-Lomagne, France and initially studied mathematics in Bordeaux with some of the disciples of Viete, a French algebraist (Katz 2009). He went on to earn a law degree and become a successful counselor. Mathematics was merely a hobby to him, so he never published because he did not want to thoroughly explain his discoveries in detail. He died in 1665 and his son later published his manuscripts and correspondence. Fermat adapted Viète’s algebra to the study of geometric loci and used letters to represent variable distances. He discovered that the study of loci, or sets of points with certain characteristics, could be made easier by applying algebra to geometry through a coordinate system (Katz 2009). Basically any relation between ...
Leonardo Pisano was the first great mathematician of medieval Christian Europe. He played an important role in reviving ancient mathematics and made great contributions of his own. After his death in 1240, Leonardo Pisano became known as Leonardo Fibonacci.
Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in the early twentieth century. Although it appears simple, the Sierpinski Triangle is actually a complex and intriguing fractal. Fractals have been studied since 1905, when the Mandelbrot Set was discovered, and since then have been used in many ways. One important aspect of fractals is their self-similarity, the idea that if you zoom in on any patch of the fractal, you will see an image that is similar to the original. Because of this, fractals are infinitely detailed and have many interesting properties. Fractals also have a practical use: they can be used to measure the length of coastlines. Because fractals are broken into infinitely small, similar pieces, they prove useful when measuring the length of irregularly shaped objects. Fractals also make beautiful art.
The Golden Ratio is a strange ratio that scientists have found all throughout nature, architecture, art, and various other places. Some say that the Golden Ratio could only have been made possible by God while others believe it is merely a coincidence. This “Golden Number” has been thought of as the most pleasing to the eye and many tests have been done to see whether humans’ perception of beauty is affected by the appearance of this phenomenon.
They constructed the 12-month calendar which they based on the cycles of the moon. Other than that, they also created a mathematical system based on the number 60 which they called the Sexagesimal. Though, our mathematics today is not based on their system it acts like a foundation for some mathematicians. They also used the basic mathematics- addition, subtraction, multiplication and division, in keeping track of their records- one of their contributions to this world, bookkeeping. It was also suggested that they even discovered the number of the pi for they knew how to solve the circumference of the circle (Atif, 2013).
The history of the computer dates back all the way to the prehistoric times. The first step towards the development of the computer, the abacus, was developed in Babylonia in 500 B.C. and functioned as a simple counting tool. It was not until thousands of years later that the first calculator was produced. In 1623, the first mechanical calculator was invented by Wilhelm Schikard, the “Calculating Clock,” as it was often referred to as, “performed it’s operations by wheels, which worked similar to a car’s odometer” (Evolution, 1). Still, there had not yet been anything invented that could even be characterized as a computer. Finally, in 1625 the slide rule was created becoming “the first analog computer of the modern ages” (Evolution, 1). One of the biggest breakthroughs came from by Blaise Pascal in 1642, who invented a mechanical calculator whose main function was adding and subtracting numbers. Years later, Gottfried Leibnez improved Pascal’s model by allowing it to also perform such operations as multiplying, dividing, taking the square root.
Addition, especially of small numbers, is a process that can be done over many repetitions. Sometimes, it produces interesting patterns. One such pattern is in Pascal’s Triangle, where each row can be constructed by adding the numbers on the row above. This particular pattern is significant in that, among other things, it shows a representation of the coefficients of a binomial expansion to a particular power.