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Fibonacci sequence speach
Fibonacci sequence speach
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Leonardo Fibonacci, also known as Fibonacci and Leonardo of Pisa, was an Italian Mathematician who lived during the 12th and 13th century. On his journey to Africa and Syrian, he learned the Arabic mathematics, which was unknown to Europeans. Fibonacci published a book called Liber Abaci which contributed to Europe adapting the Arabic system of numbers. Liber Abaci included a thought experiment that later became known as the Fibonacci sequence. In his thought experiment, Fibonacci wanted to calculate the number rabbits that could originate from one pair of rabbits in one year. He assumed that none of the rabbits would die and each pair would produce exactly one pair of both sexes as soon as they matured at one month. After one month there are …show more content…
Fibonacci observed that to find the number of rabbits one can calculate the sum of the pairs of rabbits of the previous two months. Starting with 1 pair, after on month there are 2 pairs, then 3, 5, 8, 13 and so on. The series was later observed in nature and art. The Fibonacci sequence also be explained using geometry. First, draw a square with the length 1, then another square next to it with same length, then another with length 3, then with length 5, then with length 8 and continue along the Fibonacci sequence. When you draw a quadrant in each square a spiral is formed, which is identical to the shells of snails and nautilus. This Fibonacci spiral can also be found in human ears, spiral galaxies, hurricanes, cauliflowers, pineapples, sunflower and each of those spirals in plants contains a number of seeds, florets, bumps or leaves that are equal to a Fibonacci number. Furthermore, when one number of the sequence is divided by the previous number and as the number increases, the result approaches 1.618, getting increasingly accurate, but never quite reaching that ratio. This ratio is known as The Golden Mean or The Devine
We put a rectangular piece of cardboard vertically in the middle of an empty rectangular box. One side of the box was filled up with damp soil, and the other side was filled with dry soil. We filled the soil up to the level of the rectangular piece of cardboard, so that the cardboard wall would not deter the sowbug from crossing. We gathered 4 sowbugs, and placed them in a petri dish. We placed the sowbugs one by one on the border between both soils. Each of us tracked one sowbug, and diagrammed the movement. Every minute we would make a mark of where the sowbug had travelled. We continued this process for five minutes. We took the sowbugs out of the chamber, and placed them back in the petri dish. We repeated the experiment under the same conditions. Because we were short on time, we kept the same sowbugs for the second experiment
Leonardo da Vinci was a famous painter, sculptor, and inventor that lived from 1452-1519. He was born in a small Italian town of Vinci and lived on a small estate that his father owned. Leonardo kept the name of the town that he was born in for his last name. Since his mother did not marry his father, he could not inherit his father’s land, nor did he have much going for him as a wealthy businessman. When people think of Leonardo da Vinci, they mostly associate him with art and paintings, such as his famous Mona Lisa and The Last Supper. Leonardo believed that art was correlated to science and nature. Da Vinci was largely self-educated and he filled endless notebooks with examinations and suppositions about pursuits from aeronautics to anatomy.
While the studies at Governor’s School are noticeably more advanced and require more effort than at regular public schools, I see this rigor as the key to my academic success. For me, the classes I take that constantly introduce new thoughts that test my capability to “think outside the box”, are the ones that capture all my attention and interest. For example, while working with the Sierpinski Triangle at the Johns Hopkins Center for Talented Youth geometry camp, I was struck with a strong determination to figure out the secret to the pattern. According to the Oxford Dictionary, the Sierpinski Triangle is “a fractal based on a triangle with four equal triangles inscribed in it. The central triangle is removed and each of the other three treated as the original was, and so on, creating an infinite regression in a finite space.” By constructing a table with the number black and white triangles in each figure, I realized that it was easier to see the relations between the numbers. At Governor’s School, I expect to be provided with stimulating concepts in order to challenge my exceptional thinking.
My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the seniors. I’m not sure exactly when simple interest turned to a kind of obsession, but during that lesson something seemed to click. It seemed as if this was the universe’s answer to everything; the mystery was solved, however complex the answer was to understand. I’m still not sure if I was misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe the way the universe works.
Similar to any branch of math or science, new concepts do not simply generate all of a sudden. Fractal ideas can be traced back to the late nineteenth century, however if one looks past that, they will see that the anchient Greek mathematicians also dabbled in the world of fractals.
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.
Phi is based on the idea of creating a ratio that makes it so that the ratio of a to b is equal to the sum of the two numbers compared to the longer side,a/b=a+b/a(Goldennumber.net, “Mathematics of Phi, the Golden Ratio”). The one solution to this problem is the number phi which is 1.61803398…phi goes on forever and never repeats. Moreover, when creating a rectangle we can make the dimensions match the golden ratio by having l to w equal to phi; a shape called the golden rectangle. You can separate this rectangle into a b x b square and a b x b-a then that b x b-a rectangle is also equal to phi. We can do the same thing again to this smaller rectangle and we can keep going on and on and this eventually creates a spiral effect, continuing on if you were to draw an arc outlining the spiral it would make the golden spiral.
‘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
One of the most common places to see Fibonacci numbers is in the growth patterns of plants. Growth spirals are characterized by both a circular motion, and elongation. As a branch grows, it produces leaves at regular intervals, but not after each complete circle of its spiral. The reason the leaves are not directly above each other is because all of the leaves would not be able to get the necessary elements. It appears that leaves are generated on the stem in phyllotactic ratios where the numerator and denominator are both Fibonacci numbers. The numerator is the number of turns, and the denominator is the number of leaves past until there is a leaf directly above the original. The number of leaves past, ad both directions of turns produce 3 consecutive Fibonacci numbers. For example, in the top plant on this transparency, there are 3 clockwise rotations before there is a leaf directly above the first leaf, passing 5 leaves along the way. Notice that 2, 3, and 5 are all consecutive Fibonacci numbers. The same is true for the bottom plant, except that it rakes 5 rotations for 8 leaves. We would write this as 3/5 clockwise rotations per leaf on the top one and 5/8 for the bottom. Although, these are just computer-generated plants, the same is true in real life. A few real life examples of these phyllotactic ratios are 2/3 elm, 1/3 black berry, 2/5 apple, 3/8 weeping willow, and 5/13 *censored* willow. Daisies display Fibonacci numbers in their own unique way. If we look at this enlarged seed head of a daisy, and took the time to count the number of seeds spiraling in clockwise and counter clockwise rotations we would arrive at 34 and 55. Note that these are consecutive Fibonacci numbers. Many other flowers e...
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.
Fibonacci Numbers originated from India hundreds of years ago. Though Fibonacci Numbers came from India, Leonardo of Pisa, better known as Fibonacci, made it known to the world. Leonardo came from a wealthy Italian family and traveled to North America to join his father. He was educated by the Moors and sent on business trips. “After returning to Pisa around 1200, Leonardo wrote his most famous literature, Liber Abaci” (Pearson). Leonardo featured a rabbit question in the book. The question was asked in a mathematical competition, he appeared in when he was young. Leonardo Fibonacci used the Fibonacci Numbers to solve it. Fibonacci Numbers is now used throughout our society.
The Fibonacci sequence has a long and complex history; its roots can be traced back to India, around 200 BC or perhaps earlier. Pingala, the author of Chandaḥśāstra, used Sanskrit poetry to find patterns between long and short syllables; he provided the first description of a binary numeral system and is given partial credit to the development of the Fibonacci sequence (Lecture 32). Virahanka was an Indian mathematician that built on Pingala’s work with poetry meters; he showed how the sequence was present in the analysis of poetry meters with short and long syllables and also provided commentary for Pingala’s work, Chandaḥśāstra (. Hemachandra, a mathematician from the state of Gujarat in India, expanded upon the work of Pingala and Virahanka. 50 years before Leonardo of Pisa would present his
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that’s how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi.