Leonardo+Fibonacci

= Leonardo Fibonacci = Sohan

__Hindu Arabic Number System__
Leonardo Fibonacci is a world-renowned mathematician who worked on the basic principlesof using the Arabic-Hindu number system and discovering the Fibonacci sequence. Many believe that Fibonacci was the first person to have a deep impact on European mathematics in the early Middle Ages using the eastern number system. This achievement was recorded in this most famous book, the //Liber Abaci// in 1202. (Clark Kimberling who is a professor at the university of Mannchester). These new numbers became highly useful because it reduced the difficulty of the math, compared to computing numbers using the Roman numerals. He did this by using only 10 digits as the basis of the number system and then to make larger numbers he would simply reuse the original digits. This was simpler than the Roman method of having different letters for each value. This impact was so large that from that moment onward most countries used the Hindu-Arabic number system.

__**Found in Nature**__ Along with new and simpler number system, Fibonacci also found the Fibonacci sequence. The can be found in all aspects of life and nature. The most common examples include the petals on the leaves and the area of the shell of a sea animal. Another use for the Fibonacci sequence is to provide answers for the numerous questions that Fibonacci addresses in his first book, //Liber Abaci//, such as the rabbit population problem. In this problem as one rabbit creates the population and creates growth there will be an increase in the number of rabbits along with the death of older rabbits. Using the sequence Fibonacci was able to account the number of rabbits born and died, thus resulting in the Fibonacci sequence: 1,1,2,3,5,8,13, etc.

__**Influence that go Beyond Fibonacci's Time:**__
Fibonacci’s sequence was incorporated into Pascal’s triangle, created several centuries after the death of Fibonacci in 1250. Other mathematicians beyond his time include Johannes Kepler who incorporated his work by finding the Golden Ratio approximately 1.618… As stated by an active stock trader Justin Kuepper, “Many more use the Fibonacci studies in conjunction with other forms of technical analysis.” This proves that Fibonacci’s work and achievements in the field of mathematics have extended its usefulness beyond the middle ages and into a variety of math and science related fields. Even in modern times, Fibonacci’s arcs help stock traders such as Kuepper understand and predict the movement of the stock.

__**Written Works**__
According to the School of Mathematics and Statistics in Scotland Fibonacci also wrote many other books such as the Practica Geometriae in 1220, the Flos in 1225, Liber Quadratorum, Di minor guisa, and the Commentary of Book X of Eclids’s Elements. Many of these books varied in topics from geometry to Diophantine equations discussing varied types of problems and theories. Each book discussed in depth different methods of solving multiple problems that had stumped previous mathematicians.

__**Example of Problem and Solution:**__
For example, one of the problems that Leonardo Fibonacci solved was using the square roots. So he devised a new method of approximating irrational square roots, such as square root of 10. The method is simply using the formula: sqrt( a2+r) = a +r/2a. The principle is shown below:

sqrt 10=? Use the next closest square root   sqrt 9=3   Subtract the original square root from the easiest one   10-9=1   Use the easier square root’s answer and multiply it by 2. 3 x 2= 6  Place the numbers in the formula   3 1/6 = 3.166666   Close to:    sqrt 10=3.16227766

__**Recognition:**__
Leonardo Fibonacci received great recognition for his work from mostly people in Europe. In 1240 The Republic of Pisa granted Fibonacci a salary honoring his accomplishments. This itself was a great accomplishment due to the fact thatrecognition from an institution on private work, especially a government, proves that Fibonacci had truly benefited the scientific and mathematical world. The statue continues to stand till this day. Frederick II also recognized Fibonacci’s genius by inviting him to a mathematical conference often calling him “Stupor Mundi (The wonder of the world).” (Gies 85) In recent times, Fibonacci’s statue was erected in the 19th century in his honor. In conclusion Fibonacci brought a new era of mathematics that we continue to use to this day. Though we may not use the Fibonacci Sequence on a daily basis, it can be found in the world around us. But the most impact Fibonacci had on our lives was the number system that all mathematicians used from his time onward. Due to his numerous recognitions and achievements he has been referred to as the “greatest European mathematician in the middle ages.” (Dr Ron Knott 45)

__**Timeline:**__
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 * < **Social, Economical, and Political Background** ||
 * < Social ||< Economical ||< Political ||
 * < Fibonacci was a trader and traveler who gained a varied perspective of the world at a young age, often referred to as Bigollo (useless trader). (Gies) ||< Fibonacci came from a rich family, the Bonacci Family, who where able to support his education in North Africa.(Gies) ||< Leonardo Fibonacci’s father was a diplomat who worked in a trading post in Bugia.(Gies) ||
 * < Using the experience of traveling he discovered new ideas in mathematics that he believed could help solve problems in the European nations. ||< Most of the economical wealth came from Fibonacci’s father, Guilielmo Fibonacci, who aided merchants in making economically smart decisions.(Gies) ||< Emperor Fredrick II recognized Fibonacci for his tremendous achievements by inviting him for dinner and conventions that promoted the work of Fibonacci.(Gies) ||
 * <  ||< Leonarod Fibonacci himself spent time as a merchant as a young adult in several different countries, increasing his familiarity with simple mathematics.(Gies) ||< Fibonacci lived in a time period where the Pope ran Italy. This was a set back to Fibonacci whose mathematical theories that existed in nature was highly disapproved by the Church. Therefore, his theories were not well known in the religious community. ||


 * **Social, Economical, and Political Impact, Contributions, and Influences on others.** ||
 * Social || Economical || Political ||
 * Fibonaci’s work influenced future mathematicians (such as Pascal and Kepler), allowing them to use many of his fundamental ideas and incorporate and expand on previous theories. || In order to make the addition and subtraction of numbers easier he used the mathematical numbers of the Hindus and Arabs, 0 to 9. This changed economics because the new numbers were used world wide, especially in economics where it would be used the most. (Gies) || With a new number system in Europe, the governments had to readjust from Latin numerals to Hind-Arabic numbers. The only instution that did not change its number system was the church who opposed Fibonacci’s number system. ||
 * Fibbonacci’s most significant impact in society is that he introduced the number system (0-9) into Europe, changing how people learn and compute mathematics. This was a major break from the traditional Roman numbers.(Gies) || The Fibonacci arc and sequences are used in current day stockbrokers who need to calculate an estimated cost of the stock. (Kueper) || Fibonacci was recognized by the government of Pisa, The Republic of Pisa, for his contributions in mathematics and was awarded a standard salary. ||
 * During Fibonaci’s time period, the Middle Ages, many of the people were dependent on the church and religion. Therefore, Fibonaci’s mathematical work was highly frowned upon until the Enlightenment period. ||  ||   ||

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=__**Quiz:**__=

1. In Leonardo Fibonacci's method of finding an approximation for square roots, what number can be used to approximate sqrt(12)? a) sqrt(11) b) sqrt(13) c) sqrt(12) d) None of the above

2. In Fibonacci's earlier life he worked as a ___ with his father. a) Merchant b) Construction worker c) Scribe d) Political Leader (Diplomat)

3. Fibonacci based the new number system off of the the a) Asian Indian number system b) Arabic number system c) Niether d) Both A and B

4. Fibonacci's work helped who find the Golden Ratio? a) Pascal b) Kepler c) Euler d) Greeks

5. Fibonacci wrote which of the books? a) Liber Abaci b) The Heart of Darkness c) Treatise of the Reflection  d) He did not right any books.

6. Who invited Fibonacci to a mathematical competition? a) Ferdinand II b) Philip the Fair c) Fredrick II d) Bismarck

7. Why was Fibonacci's mathamatical work despised in his time period? a) His did not affect anybody b) The Pope did not like his rational work. c) His books were found anywhere in Italy d) The mathematical work did not make sense.

8. What does this picture of the flower (on the right) have anything to do with Fibonacci's work. (Open ended/Free responce)

9. True or False. Fibonacci found the Golden Ratio. a) True b) False

10. Fibonacci's work on arcs can be found in... a) Stock market b) Daily life c) Nature d) All of the above

Answer: 1.D 2.A 3.D 4.B 5.A 6.C 7.B 8. The fibonacci sequence can be found in nature. For example, in the flower if you count the petals clockwise, you can find the last number is a fibonacci number and if you count counter clockwise, you will find that its last number is a next number in the Fibonacci sequence. 9. F 10. D

Picture Bibliography: Britton, Ian. //Sunflowers//. October 23, 2003. //Free Foto//. Web. 7 Mar. 2011. . //Fibonacci Phyllotaxis//. June 20, 2006. //Flicr CC//. Web. 7 Mar. 2011. . //Fibonacci Spiral//. March 8, 2009. //Texample//. Web. 7 Mar. 2011. . //Leonardo Fibonacci//. 19th Century. //Wikipedia commons//. Web. 7 Mar. 2011. . //Leonardo Fibonacci//. 19th Century. //Wikipedia Commons//. Web. 7 Mar. 2011. . Navaneethakrishnan, Kumar. //Fibonacci Numbers//. N.d. //fotopedia//. Web. 7 Mar. 2011. . //Numbers//. 2009. //Photography Section//. Web. 7 Mar. 2011. .

Research Bibliography: “FIbonacci Biography.” //School of Mathamatics and Statistics//. University of St. Andrews, Scotland, n.d. Web. 18 Mar. 2011. . “Fibonacci Sequence.” //Math is Fun//. N.p., n.d. Web. 18 Mar. 2011. . “Fibonacci Sequence (PRIME).” //Platonic Realms//. N.p., n.d. Web. 18 Mar. 2011. . Gies, Joseph, and Frances Gies. //Leonardo de PIsa//. N.p.: n.p., n.d. Print. Knott, Ron. “Who was Fibonacci.” //Math UK//. N.p., n.d. Web. 18 Mar. 2011. .