The Leaning Tower Of Pisa, Italy

Leonardo Fibonacci When thinking of Pisa, Italy, one of the first things that comes to mind is the Leaning Tower of Pisa. The Leaning Tower of Pisa is known worldwide for gradually increasing its vertical offset over the hundreds of years it has been standing. The Leaning Tower is just one of many historical landmarks and striking artworks in Pisa, Italy; however no one would think of a marble sculpture of Leonardo Fibonacci by Giovanni Paganucci when thinking of Pisa (Long 4). The marble statue of Leonardo is located in the Camposanto in Pisa and was finished by Paganucci in 1863 (Long 4). Leonardo Fibonacci is known by most people for the Fibonacci sequence. Besides fact that Leonardo was a mathematician, most people do not know much

While in the city Leonardo continued his education from a Moorish Schoolmaster (King 33) and he learned Arabic, as it was the main language of Bugia (Aczel 66). After completing his education, Leonardo went on a voyage around the Mediterranean that lasted a few years, making stops at Syria, Greece, Egypt, Sicily, and Constantinople (King 66). While on this journey, he studied with Arab mathematicians (Aczel 66) and became familiar with Hindu-Arabic numerals (Aczel 67). After his voyage, Leonardo returned to Pisa, Italy in 1200 (Aczel 67) and began compiling all that he had learned. Then in 1202, Leonardo published Liber Abaci, Book of the Abacus (McClenon 143). In the Liber Abaci, Leonardo contained the Hindu-Arabic numeral system, which is 1, 2,3,4,5,6,7,8,9. Leonardo also introduced zero, 0 (Aczel 67). The significance of the Liber Abaci is not that it is the first book written in Italy that had the Hindu-Arabic numeral system, but it is the first book that contains examples of the system being used in problems (McCleanon 143). This allowed readers to learn the Hindu-Arabic system as well. Also in the Liber Abaci is Leonardo’s famous problem which contains the Fibonacci sequence. The problem is stated as follows (Gies

As the Fibonacci numbers increase, the ratios of the numbers become closer to the Golden Ratio. As a result of the Fibonacci sequence numbers’ ratios being close to the Golden Ratio, Fibonacci numbers often occur in nature. Examples of these are the spirals on pineapples, pine cones, and palm leaves; they all occur in Fibonacci numbers (Posamentier 64, 65). Many flowers, including Daisies and Sunflowers, are in spirals that are Fibonacci numbers. The sunflower’s seeds commonly occur in 34 and 55, while the daisy’s petals are commonly found to have 13 and 21 or 21 and 34 (Newton 5). Fibonacci numbers occur in nature in other ways besides plants. In the hydrogen gas atom, when the gas gains radiant energy, and when it loses radiant energy, occurs in Fibonacci numbers (Huntley 523). Also the genealogical tree of the male bee occurs in Fibonacci numbers (Basin 53), as well as the spiral of a snail