Wait a second!
More handpicked essays just for you.
More handpicked essays just for you.
Mathematical concepts related to Fibonacci sequence
Don’t take our word for it - see why 10 million students trust us with their essay needs.
Recommended: Mathematical concepts related to Fibonacci sequence
Fibonacci numbers are not ordinary numbers
This number system was developed by Leonardo Pisano and pertains to many facets of our world today. Although this system may have many applications, it is unfortunate that not everyone knows about it. If people would just stop and apply this system to their everyday lives it would enable them to see the world differently. It all started back in the year twelve hundred and two, when a mathematician by the name of Leonardo Pisano, who came to be known as Fibonacci, wrote a book which he entitled “Liber Abaci”. Liber Abaci translated means “book of calculations”. The book has a compilation of mathematical problems he solved using his system of numbers. To find these numbers one would add two consecutive numbers and your answer will give you the number you are looking for (e.g. zero, one, one, two, three, five, eight, thirteen, etc.). Knott et al. (2013) stated that the book proved to be a great mathematical achievement by introducing the decimal number system to the Latin speaking world (p.1). Fibonacci numbers are a set of numbers that changed the mathematic world for the better.
Fibonacci was born Leonardo Pisano in the twelfth century in the Italian city of Pisa. Pisano was educated in Northern Africa where he grew up. After spending many years traveling he returned to Pisa in the year twelve hundred. Upon his return he decided to pass the knowledge he gained to the public of Pisa, in the form of his book. The name Fibonacci was given to Leonardo when a group of scholar’s mistook his title to be his name. Fibonacci had intended his book to make mathematical calculations easier through this new number system that by all accounts was superior to the Roman one. Fibonacci wou...
... middle of paper ...
...ay in many facets of the world we live in. Especially in nature, we see the systems in such things such as petals on flowers, spirals on shells, seed patterns, to the spiral of falcons. Many other equations and formulas were derived from these properties. Although most people still do not know about the Fibonacci numbers, if we continue to spread the word and enlighten others, everyone will benefit and be able to see the world mathematically.
Works Cited
Knott, R., & the Plus team (2013). The life and numbers of Fibonacci. Retrieved from http://plus.math.org/content/life-and-numbers-fibonacci Childs, M., Gavra, A., Hua, J., & Vesuna, J. (2009). Fabulous Fibonacci. Retrieved from http://www.fabulousfibonacci.com/portal/
Encyclopedia Britannica (2014). Online encyclopedia. Retrieved from http://www.britannica.com/EBchecked/topic/205791/Fibonacci-numbers
Rubba, J. (1997, February 3). Ebonics: Q & A. Retrieved July 12, 2010, from http://www.cla.calpoly.edu/~jrubba/ebonics.html
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
Link, B. G., Struening, E. L., Neese-Todd, S., Asmussen, S., & Phelan, J. C. (2001). The
The Fibonacci Sequence was discovered by Leonardo Fibonacci. It is a sequence of numbers in which the next number is the sum of the two numbers previous to it. There is a direct correlation between this sequence of numbers and the Golden Ratio. If you were to take two adjacent numbers in the Fibonacci sequence and divide them, their ratio would be very close to the Golden Ratio. Also, as the numbers get higher, their ratios get closer to the golden ratio itself. For example, the ratio of 5 to 3 is 1.666… But the ratio of 21 to 12 is 1.615… Getting even higher, the ratio of 233 to 144 is
...t. The Chaos Game can be applied to create other fractals and shapes, and is a major part of an entirely separate area of study: chaos theory. The fact that the Sierpinski Triangle transcends the boundaries of fractal and number theory proves that it is an important part of mathematics. Perhaps the Sierpinski Triangle still holds secrets that, if discovered, will change the way we think about mathematics forever.
Blaise Pascal has contributed to the field of mathematics in countless ways imaginable. His focal contribution to mathematics is the Pascal Triangle. Made to show binomial coefficients, it was probably found by mathematicians in Greece and India but they never received the credit. To build the triangle you put a 1 at the top and then continue placing numbers below it in a triangular pattern. Each number is the two numbers above it added together (except for the numbers on the edges which are all ‘1’). There are patterns within the triangle such as odds and evens, horizontal sums, exponents of 11, squares, Fibonacci sequence, and the triangle is symmetrical. The many uses of Pascal’s triangles range from probability (heads and tails), combinations, and there is a formula for working out any missing value in the Pascal Triangle: . It can also be used to find coefficients in binomial expressions (put citation). Another staple of Pascal’s contributions to projective geometry is a proof called Pascal’s theore...
‘Nature abounds with example of mathematical concepts’ (Pappas, 2011, .107). It is interesting how much we see this now we know, regarding the Fibonacci Sequence, which is number pattern where the first number added to itself creates a new number, then adding that previous number to the new number and so on. You will notice how in nature this sequence always adds up to a Fibonacci number, but alas this is no coincidence it is a way in which plants can pack in the most seeds in a small space creating the most efficient way to receive sunlight and catches the most
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
Arabic numbers make mathematics much easier. (Kestenbaum, 2012) One of the first books printed on the Gutenburg printing press was Luca Pacioli’s book about double entry accounting in 1494. David Kestenbaum explains Luca Pacioli’s double entry accounting with the following quote: Every transaction gets entered twice in financial records. If one day you sold three gold coins worth of pepper, you would write that the amount of cash you had went up by three gold coins.
The recursive sequence of numbers that bear his name is a discovery for which Fibonacci is popularly known. While it brought him little recognition during the course of his life, is was nearly 100 years later when the majority of the mathematicians recognized and appreciated his invention. This fascinating and unique study of recursive numbers possess all sorts of intriguing properties that can be discovered by applying different mathematical procedures to a set of numbers in a given sequence. The recursive / Fibonacci numbers are present in everyday life and they are manifested in the everyday life in which we live. The formed patterns perplex and astonish the minds in real world perspectives. The recursive sequences are beautiful to study and much of their beauty falls in nature. They highlight the mathematical complexity and the incredible order of the world that we live in and this gives a clear view of the algorithm that God used to create some of these organisms and plants. Such patterns seem not have been evolved by accident but rather, they seem to have evolved by the work of God who created both heaven and
In the Roman civilization there was no symbol for zero. Romans used the word “nulla” for an empty space. The word nulla meant “nothing”; what our common day zero means. Romans had a very unorganized number system. It was full of flaws. With no use of zero, there was absolutely no way for counting above several thousand units. When the Roman Empire fell in 300 A.D., the introduction and adaptation of Arabic numerals, today's decimal numbers, took place. Thus, the invention of zero, nothing, was a huge leap forward in Roman history.
Gardner, Martin. "MATHEMATICAL GAMESThe Fantastic Combinations of John Conway's New Solitaire Game "life"" Scientific American 223.4 (1970): 120-23. Conway's Game of Life: Scientific American, October 1970. Web. 24 Mar. 2014.
Irrational numbers are real numbers that cannot be written as a simple fraction or a whole number. For example, irrational numbers can be included in the category of √2, e, Π, Φ, and many more. The √2 is equal to 1.4142. e is equal to 2.718. Π is equal to 3.1415. Φ is equal to 1.6180. None of these numbers are “pretty” numbers. Their decimal places keep going and do not end. There is no pattern to the numbers of the decimal places. They are all random numbers that make up the one irrational number. The concept of irrational numbers took many years and many people to discover and prove (I.P., 1997).
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
As mathematics has progressed, more and more relationships have ... ... middle of paper ... ... that fit those rules, which includes inventing additional rules and finding new connections between old rules. In conclusion, the nature of mathematics is very unique and as we have seen in can we applied everywhere in world. For example how do our street light work with mathematical instructions? Our daily life is full of mathematics, which also has many connections to nature.