Pamela Dela Cruz
Math 150A
M/Tu/W/F 10-10:50am.
12/10/12
Leonardo Piscano Fibonacci In 1170, Leonardo Piscano Fibonacci, more commonly referred to as Fibonacci, was born in Pisa, Italy to Guilielmo, a member of the Bonacci family. Guilielmo held a position as a secretary of the Republic of Pisa, in the province of Tuscany. In 1192, Guilielmo was posted to trading center in the city of Bugia in North Africa. After accepting this job, Guiliemo brought Fibonacci with him1. Here, Fibonacci was taught his education. He continued to learn more as he grew motivation to mathematical inquiry from traveling around other countries with his father2. Somewhere in between Barbary and Constantinople, he had become familiar with the Hindu/Arabic numeral system and discovered its enormous practical advantages compared to the Roman Numerals. He had ended his travels in 1200 and returned back to Pisa. For the next 25 years, he wrote a number of texts that played an important role in reviving ancient mathematical skills or contributed to the making of his own1. Four of which became the major components to his surviving work. In 1202, he released his first major work, “Liber Abbaci” or “The Book of Calculations”. It had presented a basic overview of basic arithmetic and algebra. However, he had also exposed a new alternative computing method for the replacement of having to use an abacus for arithmetical operations and was based on written algorithms rather counting objects. First, he discussed common finger computations and the use of Roman numerals as they were common to Europe at that time. Then he introduced the Hindu/Arabic numerals and describes the Arabic rules to working with them. The book also examined root extraction, a variety of word problems, and practical problems of value to the merchants at that time for the calculation of interest or problems that concerned exchange rates and profit margins. Fibonacci composed his second work in 1220-1221, and was called “Practica Geometriae”. The work primarily focuses on the works of ancient Greek masters such as Euclid, Archimedes, and Plato of Tivoli. The book’s discussion is predominantly on quadratic equations and the examination of solutions. It also gives instructions for a practical surveyor, the explanations to others’ work, and indeterminate problems. In 1225, his work, “Flo” was sent to Emperor Fredrick II as a response to problems set forth by Johannes of Palermo. He had showed that the solution to the equation was not a whole, fraction, or any of Euclidean irrational magnitudes, but a rational approximation of the solution. The third and final problem is the solution to a series of indeterminate equations. His fourth major work was composed in 1225 and was called “Liber Quadatorum”. It contained his acheivements in number theory and gave a variety of methods for finding Pythagorean triples. It also had a definition for a special class of numbers he called a congruum and a proof that obtained the full solution to set of equations from Johannes of Palermo. These two works showed his ability to solve algebraic equations on a higher degree1. Fibonacci had passed away in 12402, but was still well known for his works as well as being recognizable for other achievements. His most famous achievement is the Fibonacci sequence as it’s considered to be his most important accomplishment to the introduction of Hindu-Arabic mathematics into western culture for being a compilation of known techniques for a new audience. He was also responsible for the introduction of Arab mathematics to Arabs since it was most commonly used by scientists and mathematicians, but not by merchants. Which also gave him credit to the introduction of scientific calculating techniques into general business practice2.

--------------------------------------------
[ 1 ]. " Fibonacci." Mathematics Department - Welcome. N.p., n.d. Web. 9 Dec. 2012. .
[ 2 ]. " Fibonacci, Leonardo da Pisa (ca. 1170-ca. 1240) -- from Eric Weisstein's World of Scientific Biography." ScienceWorld. N.p., n.d. Web. 9 Dec. 2012. .